7th Grade Math Quiz: Understand Probability As Number 0 1

What this quiz covers

This quiz focuses on Understand Probability As Number 0 1, giving you a quick way to practice the rules, question types, and explanations that matter most for 7th Grade Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

Question 1

1. Drawing blue has probability $\frac{3}{5}$ and is more likely than drawing red (correct answer)
2. Drawing blue has probability $\frac{2}{3}$ and is much more likely than drawing red
3. Drawing blue has probability $\frac{1}{5}$ and is much less likely than drawing red
4. Drawing blue has the same probability as red since both are around $\frac{1}{2}$

Explanation: Since there are only red and blue marbles, P(blue) = 1 - P(red) = 1 - 2/5 = 3/5. Since 3/5 > 2/5, blue is more likely. Choice B uses wrong probability calculation. Choice C incorrectly calculates P(blue). Choice D incorrectly states 2/5 is around 1/2.

Question 2

1. $0.03$, $0.49$, $0.91$
2. $0.91$, $0.49$, $0.03$ (correct answer)
3. $0.49$, $0.91$, $0.03$
4. $0.91$, $0.03$, $0.49$

Explanation: Larger probability numbers indicate greater likelihood. Since 0.91 > 0.49 > 0.03, the correct order from most likely to least likely is 0.91, 0.49, 0.03. Choice A shows least to most likely. Choices C and D have incorrect orderings.

Question 3

1. Both prizes are less likely than an event that is neither likely nor unlikely (correct answer)
2. The small prize is more likely, and the large prize is less likely than neither likely nor unlikely
3. Both prizes are more likely than an event that is neither likely nor unlikely
4. The large prize is more likely, and the small prize is less likely than neither likely nor unlikely

Explanation: An event that is neither likely nor unlikely has probability around 1/2 = 6/12. Small prize: 5/12 < 6/12, Large prize: 1/6 = 2/12 < 6/12. Both are less than 1/2. Choice B incorrectly states small prize is more likely. Choices C and D incorrectly compare the probabilities to 1/2.

Question 4

1. Products are likely to have defects since the probability is greater than zero
2. Products are very likely to have defects since $\frac{11}{50}$ is a large fraction
3. Products have an equal chance of having or not having defects
4. Products are unlikely to have defects since $\frac{11}{50} = 0.22$ is close to zero (correct answer)

Explanation: When you encounter probability questions, you need to interpret what the numerical value actually means in real-world terms. Converting fractions to decimals often makes this interpretation clearer. First, let's convert $\frac{11}{50}$ to a decimal: $\frac{11}{50} = 0.22 = 22\%$. This means that out of every 100 products, about 22 would have defects while 78 would not. Since significantly more products (78%) are defect-free than defective (22%), products are unlikely to have defects. Answer D correctly identifies this pattern and explains that 0.22 is relatively close to zero. Let's examine why the other choices miss the mark. Choice A makes a logical error—just because a probability is greater than zero doesn't mean an event is likely. Most probabilities are greater than zero, but many events remain unlikely. Choice B incorrectly calls $\frac{11}{50}$ a "large fraction" when it's actually less than half, making it relatively small. Choice C suggests equal chances (50-50), but $\frac{11}{50} = 22\%$ is nowhere near 50%. The key insight is understanding probability ranges: values close to 0 indicate unlikely events, values around 0.5 suggest roughly equal chances, and values close to 1 indicate likely events. Since 0.22 is much closer to 0 than to 0.5, the event is unlikely. Study tip: Always convert fractions to percentages in probability problems—it makes interpretation much clearer. Remember that "unlikely" doesn't mean "impossible," just that the event happens less than half the time.

Question 5

1. The probability $0.6$ is actually impossible since it's greater than $\frac{1}{2}$
2. The probability should be written as $60\%$ to determine if it's likely or unlikely
3. The reasoning is correct because unlikely events have probabilities above $0.5$
4. Probabilities above $0.5$ indicate likely events, so the event probably will happen (correct answer)

Explanation: When you encounter probability questions, remember that probabilities range from 0 to 1, where values closer to 1 indicate more likely events and values closer to 0 indicate less likely events. The key threshold is 0.5 (or 50%) - this is the dividing line between likely and unlikely events. A probability of 0.6 means the event has a 60% chance of occurring. Since 0.6 is greater than 0.5, this event is actually likely to happen, not unlikely. The student's reasoning contains a fundamental misunderstanding: they correctly identified that 0.6 is "more than half" but then incorrectly concluded this means the event "probably won't happen." In reality, when something is more than half likely, it probably will happen. Looking at the wrong answers: Choice A incorrectly states that 0.6 is impossible - probabilities between 0 and 1 are perfectly valid. Choice B suggests the format matters for determining likelihood, but whether you write 0.6 or 60%, the likelihood remains the same. Choice C contains the same error as the student's original reasoning, claiming unlikely events have probabilities above 0.5, which is backwards. Choice D correctly identifies that probabilities above 0.5 indicate likely events, making this event probable rather than improbable. Study tip: Remember the 0.5 rule - probabilities above 0.5 mean "likely" (more than 50-50 odds), while probabilities below 0.5 mean "unlikely." Don't let the decimal format confuse you; 0.6 = 60% = likely.

Question 6

1. $0.15$ (correct answer)
2. $0.48$
3. $0.52$
4. $0.85$

Explanation: A probability near 0 indicates an unlikely event. 0.15 is close to 0, making it unlikely but not impossible. Choice B (0.48) is close to 1/2, indicating neither unlikely nor likely. Choice C (0.52) is also close to 1/2 and slightly likely. Choice D (0.85) is close to 1, indicating a likely event.

Question 7

1. Rain is unlikely because the fraction has a large denominator
2. Rain is neither likely nor unlikely since it's expressed as a fraction
3. Rain is likely because $\frac{7}{8} = 0.875$ is close to 1 (correct answer)
4. Rain is impossible because probabilities must be whole numbers

Explanation: 7/8 = 0.875, which is very close to 1. Probabilities near 1 indicate likely events. Choice A incorrectly focuses on the denominator size. Choice B incorrectly suggests the format affects likelihood. Choice D incorrectly states probabilities must be whole numbers.

Question 8

1. Player B is best because fractions are always higher than decimals or percents
2. Player C is best with $0.42$, then Player A with $40\%$, then Player B with $\frac{3}{8}$ (correct answer)
3. All three players perform equally since their probabilities are all close to $\frac{1}{2}$
4. Player A is best because $40\%$ is the largest number shown

Explanation: Converting to decimals: 40% = 0.40, 3/8 = 0.375, and 0.42 = 0.42. Since 0.42 > 0.40 > 0.375, Player C is best. Choice A incorrectly assumes fractions are always largest. Choice C incorrectly treats different values as equal. Choice D compares the numerical digits rather than the actual values.

Question 9

1. $1.5$ (likely)
2. $\dfrac{1}{2}=0.5$ (equally likely)
3. $\dfrac{1}{6}\approx 0.17$ (unlikely) (correct answer)
4. $0$ (impossible)

Explanation: This question tests understanding probability as a number between 0 and 1 indicating event likelihood: 0=impossible, near 0=unlikely, 1/2=equally likely as not, near 1=likely, 1=certain, with larger numbers meaning greater likelihood. Probability scale 0 to 1: impossible events P=0 (cannot occur: rolling 7 on standard die), certain events P=1 (must occur: rolling 1-6 on die covers all outcomes), unlikely events P near 0 (like P=0.1 or 1/10: could happen but probably won't), equally likely P=1/2 (50-50: coin flip heads), likely events P near 1 (like P=0.9: probably will occur); larger probability→greater likelihood (P=0.7 means 70% chance, more likely than P=0.3 at 30%); number line: plot probabilities from 0 (left, impossible) to 1 (right, certain), 1/2 at center (neither unlikely nor likely). For example, rolling a 1 on a die has P=1/6≈0.17 (1 favorable out of 6 total outcomes, 17% chance, unlikely—closer to 0 than 0.5); flipping heads P=1/2 (equally likely as tails, 50-50); drawing a non-Ace P=48/52≈0.92 (likely—only 4 Aces so 48 out of 52 non-Ace, 92% chance); rolling a 7 is impossible P=0 (no 7 on standard die). The correct probability is 1/6≈0.17 (unlikely) as there is 1 favorable outcome out of 6 equally likely ones. A mistake is claiming P=1.5 (likely), but probabilities can't exceed 1; or confusing with impossible (P=0) when it is possible but unlikely. Steps: (1) sample space {1,2,3,4,5,6}, (2) favorable: {1}, (3) P=1/6, (4) unlikely since <0.5, (5) near 0 on line. Unlikely means possible but low chance, unlike impossible.

Question 10

1. Three-quarters of the way from 0 to 1, closer to 1 (correct answer)
2. Exactly at $\frac{1}{2}$, because $0.75=0.5$
3. Near 0, because $0.75$ is less than $\frac{1}{2}$
4. To the right of 1, because $0.75$ is greater than 1

Explanation: This question tests understanding probability as a number between 0 and 1 indicating event likelihood: 0 means impossible, near 0 means unlikely, 1/2 means equally likely as not, near 1 means likely, and 1 means certain, with larger numbers meaning greater likelihood. On the probability scale from 0 to 1, impossible events have P=0 (cannot occur, like rolling a 7 on a standard die), certain events have P=1 (must occur, like rolling a number from 1 to 6 on a die which covers all outcomes), unlikely events have P near 0 (like P=0.1 or 1/10, could happen but probably won't), equally likely events have P=1/2 (50-50, like a coin flip landing heads), and likely events have P near 1 (like P=0.9, probably will occur); larger probabilities indicate greater likelihood (P=0.7 means 70% chance, more likely than P=0.3 at 30%), and on a number line, probabilities are plotted from 0 (left, impossible) to 1 (right, certain) with 1/2 at the center (neither unlikely nor likely). For example, rolling a 1 on a die has P=1/6≈0.17 (1 favorable out of 6 total outcomes, 17% chance, unlikely—closer to 0 than 0.5); flipping heads has P=1/2 (equally likely as tails, 50-50); drawing a non-Ace from a deck has P=48/52≈0.92 (likely—only 4 Aces so 48 out of 52 are non-Ace, 92% chance); rolling a 7 is impossible with P=0 (no 7 on a standard die). In this case, 0.75 should be located three-quarters of the way from 0 to 1, closer to 1, indicating likely. A common error is placing it near 0 because 0.75<1/2 (wrong, since 0.75>0.5) or at 1/2 because 0.75=0.5 (incorrect equality), or to the right of 1 because >1 (but probabilities can't exceed 1). To use probability: (1) identify the event and sample space, (2) count favorable and total outcomes, (3) calculate P=favorable/total, (4) interpret (e.g., 0.75 near 1, likely), (5) locate on the 0-1 scale (three-quarters toward 1). Comparing probabilities: larger means more likely (if P(rain)=0.3 and P(sun)=0.7, sun is more likely since 0.7>0.3); complementary events sum to 1 (if P(A)=0.3, P(not A)=0.7); impossible (P=0 exactly, like rolling 7) differs from unlikely (P>0 but near 0, like rolling 1); mistakes include probabilities outside 0-1, wrong likelihood categories, backward comparisons, or confusing percent with probability.

Question 11

1. Rain is impossible because 0.30 is close to 0
2. Rain is somewhat unlikely (less than a 50% chance) (correct answer)
3. The probability should be 30, not 0.30
4. Rain is certain because 0.30 is close to 1

Explanation: This question tests understanding probability as number 0-1 indicating event likelihood: 0=impossible, near 0=unlikely, 1/2=equally likely as not, near 1=likely, 1=certain, with larger numbers meaning greater likelihood. Probability scale 0 to 1: impossible events P=0 (cannot occur: rolling 7 on standard die), certain events P=1 (must occur: rolling 1-6 on die covers all outcomes), unlikely events P near 0 (like P=0.1 or 1/10: could happen but probably won't), equally likely P=1/2 (50-50: coin flip heads), likely events P near 1 (like P=0.9: probably will occur); larger probability→greater likelihood (P=0.7 means 70% chance, more likely than P=0.3 at 30%); number line: plot probabilities from 0 (left, impossible) to 1 (right, certain), 1/2 at center (neither unlikely nor likely). For example, rolling 1 on die has P=1/6≈0.17 (1 favorable of 6 total outcomes, 17% chance, unlikely—closer to 0 than 0.5); flipping heads P=1/2 (equally likely as tails, 50-50); drawing non-Ace P=48/52≈0.92 (likely—only 4 Aces so 48 of 52 non-Ace, 92% chance); rolling 7 impossible P=0 (no 7 on standard die). The correct interpretation is that rain is somewhat unlikely with less than a 50% chance, as 0.30 is between 0 and 0.5. Common errors include calling 0.30 certain (wrong, it's not close to 1) or impossible (it's >0), confusing with percent like saying it should be 30 not 0.30, or misinterpreting likelihood (0.30 as likely when it's unlikely). To use probability: (1) identify event (rain tomorrow), (2) the app provides P=0.30, (3) no calculation needed, (4) interpret (0.30 near 0 but >0, unlikely), (5) locate on 0-1 scale (between 0 and 0.5, closer to unlikely). Comparing: larger probability more likely (P(rain)=0.3 vs P(no rain)=0.7, no rain more likely); mistakes include interpreting small P as likely or confusing decimal with whole number.

Question 12

1. Mia: $P=50$, Noah: $P=10$; Mia is more likely
2. Mia: $P=0.50$, Noah: $P=0.10$; Mia is more likely (correct answer)
3. Mia: $P=0.10$, Noah: $P=0.50$; Noah is more likely
4. Mia: $P=1.50$, Noah: $P=0.10$; Mia is more likely

Explanation: This question tests understanding probability as number 0-1 indicating event likelihood: 0=impossible, near 0=unlikely, 1/2=equally likely as not, near 1=likely, 1=certain, with larger numbers meaning greater likelihood. Probability scale 0 to 1: impossible events P=0 (cannot occur: rolling 7 on standard die), certain events P=1 (must occur: rolling 1-6 on die covers all outcomes), unlikely events P near 0 (like P=0.1 or 1/10: could happen but probably won't), equally likely P=1/2 (50-50: coin flip heads), likely events P near 1 (like P=0.9: probably will occur); larger probability→greater likelihood (P=0.7 means 70% chance, more likely than P=0.3 at 30%); number line: plot probabilities from 0 (left, impossible) to 1 (right, certain), 1/2 at center (neither unlikely nor likely). For example, rolling 1 on die has P=1/6≈0.17 (1 favorable of 6 total outcomes, 17% chance, unlikely—closer to 0 than 0.5); flipping heads P=1/2 (equally likely as tails, 50-50); drawing non-Ace P=48/52≈0.92 (likely—only 4 Aces so 48 of 52 non-Ace, 92% chance); rolling 7 impossible P=0 (no 7 on standard die). The correct statement is Mia P=0.50, Noah P=0.10, Mia more likely since 0.50>0.10. Common errors include using percents as probabilities like P=50 or 10 (wrong, should be 0.50 and 0.10), backward comparison (Mia 0.10, Noah 0.50), or invalid P=1.50 (>1). To use probability: (1) identify sample space (100 tickets), (2) favorable for Mia (50), Noah (10), (3) P(Mia)=50/100=0.50, P(Noah)=10/100=0.10, (4) interpret (0.50 equal, 0.10 unlikely), (5) compare (0.50>0.10). Comparing: larger P more likely; mistakes include confusing percent with probability or invalid values.

Question 13

1. $\frac{1}{2}$ (correct answer)
2. $-\frac{1}{2}$
3. $1$
4. $2$

Explanation: This question tests understanding probability as a number between 0 and 1 indicating event likelihood: 0 means impossible, near 0 means unlikely, 1/2 means equally likely as not, near 1 means likely, and 1 means certain, with larger numbers meaning greater likelihood. On the probability scale from 0 to 1, impossible events have P=0 (cannot occur, like rolling a 7 on a standard die), certain events have P=1 (must occur, like rolling a number from 1 to 6 on a die which covers all outcomes), unlikely events have P near 0 (like P=0.1 or 1/10, could happen but probably won't), equally likely events have P=1/2 (50-50, like a coin flip landing heads), and likely events have P near 1 (like P=0.9, probably will occur); larger probabilities indicate greater likelihood (P=0.7 means 70% chance, more likely than P=0.3 at 30%), and on a number line, probabilities are plotted from 0 (left, impossible) to 1 (right, certain) with 1/2 at the center (neither unlikely nor likely). For example, rolling a 1 on a die has P=1/6≈0.17 (1 favorable out of 6 total outcomes, 17% chance, unlikely—closer to 0 than 0.5); flipping heads has P=1/2 (equally likely as tails, 50-50); drawing a non-Ace from a deck has P=48/52≈0.92 (likely—only 4 Aces so 48 out of 52 are non-Ace, 92% chance); rolling a 7 is impossible with P=0 (no 7 on a standard die). In this case, the correct probability of landing heads on a fair coin is 1/2, as it is equally likely to happen or not. A common error is claiming P=1 (thinking heads is certain) or P=-1/2 (using negative for unlikely, but probabilities can't be negative), or P=2 (exceeding the maximum of 1). To use probability: (1) identify the event and sample space (coin flip: sample space {heads, tails}), (2) count favorable and total outcomes (heads: 1 favorable, 2 total), (3) calculate P=favorable/total (1/2), (4) interpret (1/2 means equally likely), (5) locate on the 0-1 scale (at center, neither unlikely nor likely). Comparing probabilities: larger means more likely (if P(rain)=0.3 and P(sun)=0.7, sun is more likely since 0.7>0.3); complementary events sum to 1 (if P(A)=0.3, P(not A)=0.7); impossible (P=0 exactly, like rolling 7) differs from unlikely (P>0 but near 0, like rolling 1); mistakes include probabilities outside 0-1, wrong likelihood categories, backward comparisons, or confusing percent with probability.

Question 14

1. More likely to lose because $0.5$ is near 0
2. Certain to win
3. Equally likely to win as to lose (correct answer)
4. Impossible to win

Explanation: This question tests understanding probability as a number between 0 and 1 indicating event likelihood: 0 means impossible, near 0 means unlikely, 1/2 means equally likely as not, near 1 means likely, and 1 means certain, with larger numbers meaning greater likelihood. On the probability scale from 0 to 1, impossible events have P=0 (cannot occur, like rolling a 7 on a standard die), certain events have P=1 (must occur, like rolling a number from 1 to 6 on a die which covers all outcomes), unlikely events have P near 0 (like P=0.1 or 1/10, could happen but probably won't), equally likely events have P=1/2 (50-50, like a coin flip landing heads), and likely events have P near 1 (like P=0.9, probably will occur); larger probabilities indicate greater likelihood (P=0.7 means 70% chance, more likely than P=0.3 at 30%), and on a number line, probabilities are plotted from 0 (left, impossible) to 1 (right, certain) with 1/2 at the center (neither unlikely nor likely). For example, rolling a 1 on a die has P=1/6≈0.17 (1 favorable out of 6 total outcomes, 17% chance, unlikely—closer to 0 than 0.5); flipping heads has P=1/2 (equally likely as tails, 50-50); drawing a non-Ace from a deck has P=48/52≈0.92 (likely—only 4 Aces so 48 out of 52 are non-Ace, 92% chance); rolling a 7 is impossible with P=0 (no 7 on a standard die). In this case, the correct interpretation of P=0.5 is equally likely to win as to lose, since it's at 1/2 on the scale. A common error is calling it impossible (confusing with 0) or certain (confusing with 1), or saying more likely to lose because 0.5 is near 0 (wrong, as 0.5 is in the middle). To use probability: (1) identify the event and sample space (spinner game: sample space {win, lose}), (2) count favorable and total outcomes (assuming fair, win: equal to lose), (3) calculate P=0.5, (4) interpret (equally likely), (5) locate on the 0-1 scale (at center). Comparing probabilities: larger means more likely (if P(rain)=0.3 and P(sun)=0.7, sun is more likely since 0.7>0.3); complementary events sum to 1 (if P(A)=0.3, P(not A)=0.7); impossible (P=0 exactly, like rolling 7) differs from unlikely (P>0 but near 0, like rolling 1); mistakes include probabilities outside 0-1, wrong likelihood categories, backward comparisons, or confusing percent with probability.

Question 15

1. $1$
2. $\frac{1}{6}$
3. $\frac{1}{2}$
4. $0$ (correct answer)

Explanation: This question tests understanding probability as a number between 0 and 1 indicating event likelihood: 0 means impossible, near 0 means unlikely, 1/2 means equally likely as not, near 1 means likely, and 1 means certain, with larger numbers meaning greater likelihood. On the probability scale from 0 to 1, impossible events have P=0 (cannot occur, like rolling a 7 on a standard die), certain events have P=1 (must occur, like rolling a number from 1 to 6 on a die which covers all outcomes), unlikely events have P near 0 (like P=0.1 or 1/10, could happen but probably won't), equally likely events have P=1/2 (50-50, like a coin flip landing heads), and likely events have P near 1 (like P=0.9, probably will occur); larger probabilities indicate greater likelihood (P=0.7 means 70% chance, more likely than P=0.3 at 30%), and on a number line, probabilities are plotted from 0 (left, impossible) to 1 (right, certain) with 1/2 at the center (neither unlikely nor likely). For example, rolling a 1 on a die has P=1/6≈0.17 (1 favorable out of 6 total outcomes, 17% chance, unlikely—closer to 0 than 0.5); flipping heads has P=1/2 (equally likely as tails, 50-50); drawing a non-Ace from a deck has P=48/52≈0.92 (likely—only 4 Aces so 48 out of 52 are non-Ace, 92% chance); rolling a 7 is impossible with P=0 (no 7 on a standard die). In this case, the correct probability of rolling a 7 is 0, as it is impossible on a standard die with faces 1 through 6. A common error is thinking it's possible with a small probability like 1/6 (confusing it with rolling a specific number that exists) or 1/2 (misapplying equal likelihood), or claiming it's certain with P=1 (ignoring the impossibility). To use probability: (1) identify the event and sample space (rolling a die: sample space {1,2,3,4,5,6}), (2) count favorable and total outcomes (rolling a 7: 0 favorable, 6 total), (3) calculate P=favorable/total (0/6=0), (4) interpret (0 means impossible), (5) locate on the 0-1 scale (at 0, impossible). Comparing probabilities: larger means more likely (if P(rain)=0.3 and P(sun)=0.7, sun is more likely since 0.7>0.3); complementary events sum to 1 (if P(A)=0.3, P(not A)=0.7); impossible (P=0 exactly, like rolling 7) differs from unlikely (P>0 but near 0, like rolling 1); mistakes include probabilities outside 0-1, wrong likelihood categories, backward comparisons, or confusing percent with probability.

Question 16

1. $1$
2. $0.25$
3. $0.50$
4. $-0.10$ (correct answer)

Explanation: This question tests understanding probability as number 0-1 indicating event likelihood: 0=impossible, near 0=unlikely, 1/2=equally likely as not, near 1=likely, 1=certain, with larger numbers meaning greater likelihood. Probability scale 0 to 1: impossible events P=0 (cannot occur: rolling 7 on standard die), certain events P=1 (must occur: rolling 1-6 on die covers all outcomes), unlikely events P near 0 (like P=0.1 or 1/10: could happen but probably won't), equally likely P=1/2 (50-50: coin flip heads), likely events P near 1 (like P=0.9: probably will occur); larger probability→greater likelihood (P=0.7 means 70% chance, more likely than P=0.3 at 30%); number line: plot probabilities from 0 (left, impossible) to 1 (right, certain), 1/2 at center (neither unlikely nor likely). For example, rolling 1 on die has P=1/6≈0.17 (1 favorable of 6 total outcomes, 17% chance, unlikely—closer to 0 than 0.5); flipping heads P=1/2 (equally likely as tails, 50-50); drawing non-Ace P=48/52≈0.92 (likely—only 4 Aces so 48 of 52 non-Ace, 92% chance); rolling 7 impossible P=0 (no 7 on standard die). The value -0.10 is not possible because probabilities must be between 0 and 1 inclusive. Common errors include thinking negative values are allowed for unlikely events (no, use small positive), or overlooking that 0.25, 0.50, and 1 are valid (0.25 unlikely, 0.50 equal, 1 certain). To use probability: (1) check if value is in [0,1], (2) -0.10 <0 so invalid, (3) no calculation, (4) interpret as impossible to have negative P, (5) valid Ps on 0-1 scale only. Mistakes: probabilities outside 0-1 range, like negative or >1.

Question 17

1. $\tfrac{1}{6}=1.6$; unlikely
2. $\tfrac{5}{6}\approx 0.83$; unlikely
3. $\tfrac{1}{6}\approx 0.17$; unlikely (correct answer)
4. $\tfrac{1}{6}\approx 0.17$; certain

Explanation: This question tests understanding probability as number 0-1 indicating event likelihood: 0=impossible, near 0=unlikely, 1/2=equally likely as not, near 1=likely, 1=certain, with larger numbers meaning greater likelihood. Probability scale 0 to 1: impossible events P=0 (cannot occur: rolling 7 on standard die), certain events P=1 (must occur: rolling 1-6 on die covers all outcomes), unlikely events P near 0 (like P=0.1 or 1/10: could happen but probably won't), equally likely P=1/2 (50-50: coin flip heads), likely events P near 1 (like P=0.9: probably will occur); larger probability→greater likelihood (P=0.7 means 70% chance, more likely than P=0.3 at 30%); number line: plot probabilities from 0 (left, impossible) to 1 (right, certain), 1/2 at center (neither unlikely nor likely). For example, rolling 1 on die has P=1/6≈0.17 (1 favorable of 6 total outcomes, 17% chance, unlikely—closer to 0 than 0.5); flipping heads P=1/2 (equally likely as tails, 50-50); drawing non-Ace P=48/52≈0.92 (likely—only 4 Aces so 48 of 52 non-Ace, 92% chance); rolling 7 impossible P=0 (no 7 on standard die). The correct probability is 1/6≈0.17, classified as unlikely since it's near 0. Common errors include classifying 1/6 as certain (wrong, not 1), 5/6≈0.83 as unlikely (wrong, that's likely for blue), or invalid 1/6=1.6 (>1). To use probability: (1) identify event and sample space (drawing tile: 6 total), (2) count favorable (red: 1), (3) calculate P=1/6≈0.17, (4) interpret (near 0, unlikely), (5) locate on 0-1 scale (first sixth, closer to 0). Complementary: P(blue)=5/6≈0.83; mistakes include wrong classification or invalid calculation.

Question 18

1. $P(\text{heads})=2$; heads is very likely
2. $P(\text{heads})=\tfrac{1}{2}$; heads is equally likely as tails (correct answer)
3. $P(\text{heads})=1$; heads is certain
4. $P(\text{heads})=-\tfrac{1}{2}$; heads is unlikely

Explanation: This question tests understanding probability as number 0-1 indicating event likelihood: 0=impossible, near 0=unlikely, 1/2=equally likely as not, near 1=likely, 1=certain, with larger numbers meaning greater likelihood. Probability scale 0 to 1: impossible events P=0 (cannot occur: rolling 7 on standard die), certain events P=1 (must occur: rolling 1-6 on die covers all outcomes), unlikely events P near 0 (like P=0.1 or 1/10: could happen but probably won't), equally likely P=1/2 (50-50: coin flip heads), likely events P near 1 (like P=0.9: probably will occur); larger probability→greater likelihood (P=0.7 means 70% chance, more likely than P=0.3 at 30%); number line: plot probabilities from 0 (left, impossible) to 1 (right, certain), 1/2 at center (neither unlikely nor likely). For example, rolling 1 on die has P=1/6≈0.17 (1 favorable of 6 total outcomes, 17% chance, unlikely—closer to 0 than 0.5); flipping heads P=1/2 (equally likely as tails, 50-50); drawing non-Ace P=48/52≈0.92 (likely—only 4 Aces so 48 of 52 non-Ace, 92% chance); rolling 7 impossible P=0 (no 7 on standard die). The correct interpretation is P(heads)=1/2, meaning heads is equally likely as tails on a fair coin. Common errors include claiming P>1 like 2 for very likely (probabilities max at 1), P<0 like -1/2 for unlikely (should be small positive), or P=1 for certain (but tails is also possible). To use probability: (1) identify event and sample space (coin flip: {heads, tails}), (2) count favorable outcomes and total outcomes (heads: 1 favorable, 2 total), (3) calculate P=1/2, (4) interpret (0.5 at center, equally likely), (5) locate on 0-1 scale (at 1/2). Complementary: if P(heads)=0.5, then P(tails)=1-0.5=0.5; mistakes include probabilities outside 0-1 or confusing equally likely with certain.

Question 19

1. They are equally likely, because $0.70+0.30=1$
2. Lose, because $0.30>0.70$
3. Lose, because probabilities must be greater than 1 to be likely
4. Win, because $0.70>0.30$ (correct answer)

Explanation: This question tests understanding probability as number 0-1 indicating event likelihood: 0=impossible, near 0=unlikely, 1/2=equally likely as not, near 1=likely, 1=certain, with larger numbers meaning greater likelihood. Probability scale 0 to 1: impossible events P=0 (cannot occur: rolling 7 on standard die), certain events P=1 (must occur: rolling 1-6 on die covers all outcomes), unlikely events P near 0 (like P=0.1 or 1/10: could happen but probably won't), equally likely P=1/2 (50-50: coin flip heads), likely events P near 1 (like P=0.9: probably will occur); larger probability→greater likelihood (P=0.7 means 70% chance, more likely than P=0.3 at 30%); number line: plot probabilities from 0 (left, impossible) to 1 (right, certain), 1/2 at center (neither unlikely nor likely). For example, rolling 1 on die has P=1/6≈0.17 (1 favorable of 6 total outcomes, 17% chance, unlikely—closer to 0 than 0.5); flipping heads P=1/2 (equally likely as tails, 50-50); drawing non-Ace P=48/52≈0.92 (likely—only 4 Aces so 48 of 52 non-Ace, 92% chance); rolling 7 impossible P=0 (no 7 on standard die). The correct comparison is win is more likely because 0.70>0.30. Common errors include backward comparison (0.30>0.70 so lose more likely), thinking sum to 1 means equally likely (no, that's complementary), or requiring P>1 for likely (invalid, max is 1). Comparing: larger probability more likely (P(win)=0.7 > P(lose)=0.3, win more likely); complementary: P(lose)=1-0.70=0.30. To use probability: (1) identify events (win or lose), (2) given P(win)=0.70, (3) calculate P(lose)=0.30, (4) interpret (0.70 near 1, likely; 0.30 near 0, unlikely), (5) locate on scale (0.70 closer to 1); mistakes include comparing backwards or invalid ranges.

Question 20

1. $\tfrac{48}{52}\approx 0.92$; likely (correct answer)
2. $\tfrac{4}{52}\approx 0.08$; very likely
3. $\tfrac{48}{52}\approx 1.50$; likely
4. $-\tfrac{48}{52}\approx -0.92$; unlikely

Explanation: This question tests understanding probability as number 0-1 indicating event likelihood: 0=impossible, near 0=unlikely, 1/2=equally likely as not, near 1=likely, 1=certain, with larger numbers meaning greater likelihood. Probability scale 0 to 1: impossible events P=0 (cannot occur: rolling 7 on standard die), certain events P=1 (must occur: rolling 1-6 on die covers all outcomes), unlikely events P near 0 (like P=0.1 or 1/10: could happen but probably won't), equally likely P=1/2 (50-50: coin flip heads), likely events P near 1 (like P=0.9: probably will occur); larger probability→greater likelihood (P=0.7 means 70% chance, more likely than P=0.3 at 30%); number line: plot probabilities from 0 (left, impossible) to 1 (right, certain), 1/2 at center (neither unlikely nor likely). For example, rolling 1 on die has P=1/6≈0.17 (1 favorable of 6 total outcomes, 17% chance, unlikely—closer to 0 than 0.5); flipping heads P=1/2 (equally likely as tails, 50-50); drawing non-Ace P=48/52≈0.92 (likely—only 4 Aces so 48 of 52 non-Ace, 92% chance); rolling 7 impossible P=0 (no 7 on standard die). The correct probability is 48/52≈0.92, described as likely since it's close to 1. Common errors include P=4/52≈0.08 as very likely (wrong, that's for ace, and it's unlikely), P≈1.50 (invalid >1), or negative P like -0.92 (invalid <0) for unlikely. To use probability: (1) identify event and sample space (drawing card: 52 total), (2) count favorable (non-ace: 48), (3) calculate P=48/52≈0.92, (4) interpret (near 1, likely), (5) locate on 0-1 scale (close to right end). Complementary: P(ace)=4/52≈0.08, P(not ace)=1-0.08=0.92; mistakes include probabilities outside 0-1 or wrong likelihood category.