ISEE Lower Level Mathematics Achievement Quiz: Favorable Outcome Probability

What this quiz covers

This quiz focuses on Favorable Outcome Probability, giving you a quick way to practice the rules, question types, and explanations that matter most for ISEE Lower Level Mathematics Achievement.

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. (\frac{3}{10})
2. (\frac{2}{3})
3. (\frac{7}{10}) (correct answer)
4. (\frac{11}{15})

Explanation: The total number of outcomes is 30, since there are 30 days in April. The favorable outcomes are the two-digit dates. These are the numbers from 10 to 30. To count them, we can calculate 30 - 10 + 1 = 21. There are 21 two-digit dates in April. The probability is (\frac{21}{30}). This fraction simplifies by dividing the numerator and denominator by 3, resulting in (\frac{7}{10}).

Question 2

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

Explanation: Let 'n' be the number of nickels. The number of pennies is '2n' since there are twice as many. The total number of coins is n + 2n = 36. Combining terms, we get 3n = 36. Dividing by 3, we find n = 12. So, there are 12 nickels. The total number of coins is 36. The probability of drawing a nickel is (\frac{12}{36}), which simplifies to (\frac{1}{3}).

Question 3

1. (\frac{9}{25})
2. (\frac{11}{25})
3. (\frac{14}{25}) (correct answer)
4. (\frac{3}{5})

Explanation: The total number of gumballs is 50. The number of gumballs that are not red is the total number of gumballs minus the number of red gumballs: 50 - 22 = 28. Alternatively, we can add the number of blue and green gumballs. Green gumballs = 50 - 22 - 18 = 10. So, non-red gumballs = 18 (blue) + 10 (green) = 28. The probability is (\frac{28}{50}), which simplifies to (\frac{14}{25}).

Question 4

1. (\frac{3}{10})
2. (\frac{3}{8})
3. (\frac{13}{40})
4. (\frac{7}{10}) (correct answer)

Explanation: First, find the total number of snacks in the machine: 12 + 15 + 13 = 40. This is the total number of outcomes. The favorable outcomes are potato chips or corn chips. The number of these is 15 + 13 = 28. The probability is the ratio of favorable outcomes to the total, which is (\frac{28}{40}). Dividing both numerator and denominator by 4 simplifies the fraction to (\frac{7}{10}).

Question 5

1. (\frac{4}{21})
2. (\frac{1}{4})
3. (\frac{5}{21}) (correct answer)
4. (\frac{1}{6})

Explanation: First, determine the total number of slips. The numbers are from 10 to 30, inclusive. The count is 30 - 10 + 1 = 21 slips. This is the total number of outcomes. Next, find the favorable outcomes: numbers divisible by 5. These are 10, 15, 20, 25, and 30. There are 5 such numbers. The probability is (\frac{5}{21}).

Question 6

1. (\frac{1}{4})
2. (\frac{1}{3})
3. (\frac{3}{4}) (correct answer)
4. (\frac{4}{5})

Explanation: First, find the total number of marbles: 8 (red) + 5 (blue) + 7 (green) = 20 marbles. The number of favorable outcomes is the number of marbles that are not blue, which is 8 (red) + 7 (green) = 15 marbles. The probability is the ratio of favorable outcomes to the total number of outcomes, which is (\frac{15}{20}). Simplified, this fraction is (\frac{3}{4}).

Question 7

1. (\frac{1}{3})
2. (\frac{1}{2}) (correct answer)
3. (\frac{2}{3})
4. (\frac{5}{6})

Explanation: A standard six-sided die has faces numbered 1, 2, 3, 4, 5, 6. The total number of outcomes is 6. The prime numbers between 1 and 6 are 2, 3, and 5. Note that 1 is not a prime number. There are 3 favorable outcomes. The probability is the number of favorable outcomes divided by the total number of outcomes, which is (\frac{3}{6}), or (\frac{1}{2}).

Question 8

1. (\frac{1}{4})
2. (\frac{1}{3})
3. (\frac{5}{12}) (correct answer)
4. (\frac{7}{12})

Explanation: First, find the number of yellow crayons. There are 24 crayons in total, with 6 red and 8 blue. The number of yellow crayons is 24 - (6 + 8) = 24 - 14 = 10. The total number of outcomes is 24. The number of favorable outcomes (picking a yellow crayon) is 10. The probability is (\frac{10}{24}), which simplifies to (\frac{5}{12}).

Question 9

1. (\frac{1}{12})
2. (\frac{1}{4})
3. (\frac{1}{3}) (correct answer)
4. (\frac{1}{2})

Explanation: The total number of possible outcomes is 12, as there are 12 sections. The favorable outcomes are the multiples of 3 between 1 and 12, which are 3, 6, 9, and 12. There are 4 favorable outcomes. The probability is the ratio of favorable outcomes to total outcomes, which is (\frac{4}{12}). This fraction simplifies to (\frac{1}{3}).

Question 10

1. (\frac{1}{11})
2. (\frac{2}{11}) (correct answer)
3. (\frac{2}{9})
4. (\frac{1}{5})

Explanation: First, count the total number of letters in 'MATHEMATICS'. There are 11 letters in total, so there are 11 possible outcomes. Next, count the number of favorable outcomes, which is the number of tiles with the letter 'M'. The letter 'M' appears 2 times. Therefore, the probability of drawing an 'M' is (\frac{2}{11}).

Question 11

1. (\frac{2}{5}) (correct answer)
2. (\frac{1}{2})
3. (\frac{3}{5})
4. (\frac{2}{3})

Explanation: First, determine the number of boys in the class. If there are 30 students in total and 18 are girls, then the number of boys is 30 - 18 = 12. The total number of possible outcomes is 30. The number of favorable outcomes (selecting a boy) is 12. The probability is (\frac{12}{30}). This fraction simplifies by dividing both the numerator and denominator by 6, which gives (\frac{2}{5}).

Question 12

1. (\frac{2}{7})
2. (\frac{4}{7})
3. (\frac{6}{7})
4. (\frac{5}{7}) (correct answer)

Explanation: This is a probability question asking you to find the likelihood of a specific outcome when selecting randomly from a group. Probability equals the number of favorable outcomes divided by the total number of possible outcomes. Let's identify which days of the week contain the letter 'd': Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday. Checking each name: Monday (yes), Tuesday (yes), Wednesday (yes), Thursday (yes), Friday (yes), Saturday (yes), Sunday (yes). Wait - let me check more carefully. The days containing 'd' are: Monday, Tuesday, Wednesday, Thursday, and Saturday. That's 5 days out of 7 total days, so the probability is $\frac{5}{7}$. Looking at the wrong answers: Choice A ($\frac{2}{7}$) suggests you only counted two days with 'd' - perhaps you only noticed obvious ones like Wednesday and Thursday. Choice B ($\frac{4}{7}$) means you missed one day, likely Saturday since the 'd' appears in the middle of "Saturday." Choice C ($\frac{6}{7}$) indicates you incorrectly included one extra day - possibly thinking Sunday contains 'd' when it contains 'n'. The correct answer is D: $\frac{5}{7}$. Strategy tip: For probability questions involving letters in words, write out each option and carefully examine the spelling. Don't rely on quick mental scanning - the letter you're looking for might appear in unexpected positions within the words. Always double-check your count of favorable outcomes before calculating the fraction.

Question 13

1. (\frac{4}{25})
2. (\frac{1}{5}) (correct answer)
3. (\frac{6}{25})
4. (\frac{1}{4})

Explanation: The total number of outcomes is 25, since there are 25 tiles. We need to find the number of perfect squares between 1 and 25, inclusive. The perfect squares are 1 (since 1x1=1), 4 (2x2), 9 (3x3), 16 (4x4), and 25 (5x5). There are 5 favorable outcomes. The probability is (\frac{5}{25}), which simplifies to (\frac{1}{5}).

Question 14

1. (\frac{9}{50})
2. (\frac{1}{5}) (correct answer)
3. (\frac{11}{50})
4. (\frac{4}{5})

Explanation: The total number of outcomes is 50. The favorable outcomes are the numbers greater than 40. These numbers are 41, 42, 43, 44, 45, 46, 47, 48, 49, and 50. There are 10 such numbers. The probability is (\frac{10}{50}), which simplifies to (\frac{1}{5}).

Question 15

1. (\frac{1}{3})
2. (\frac{2}{5}) (correct answer)
3. (\frac{1}{2})
4. (\frac{3}{5})

Explanation: The total number of employees is 45. To find the number of employees who are age 30 or older, we subtract the number of employees under 30 from the total: 45 - 27 = 18. These 18 employees are the favorable outcomes. The probability is (\frac{18}{45}). Both 18 and 45 are divisible by 9. (18 \div 9 = 2) and (45 \div 9 = 5). So the simplified probability is (\frac{2}{5}).

Question 16

1. (\frac{1}{5})
2. (\frac{3}{10})
3. (\frac{1}{3})
4. (\frac{1}{2}) (correct answer)

Explanation: The total number of sections on the spinner is 10. The number of red and blue sections is 3 + 2 = 5. To find the number of yellow sections, subtract this from the total: 10 - 5 = 5. So, there are 5 yellow sections. The probability of landing on yellow is the number of yellow sections divided by the total number of sections, which is (\frac{5}{10}). This fraction simplifies to (\frac{1}{2}).

Question 17

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

Explanation: When you see a probability question asking for something "not" happening, you're dealing with complement probability. The key insight is that all possible outcomes must add up to 1, so P(not angelfish) = 1 - P(angelfish). First, find the total number of fish: 12 guppies + 8 angelfish + 4 catfish = 24 fish total. The probability of catching an angelfish is $\frac{8}{24} = \frac{1}{3}$. Therefore, the probability of NOT catching an angelfish is $1 - \frac{1}{3} = \frac{2}{3}$. You can also solve this directly by counting fish that aren't angelfish: 12 guppies + 4 catfish = 16 non-angelfish out of 24 total, giving $\frac{16}{24} = \frac{2}{3}$. Looking at the wrong answers: Choice B ($\frac{1}{2}$) might come from incorrectly thinking there are equal numbers of angelfish and non-angelfish, or from dividing 12 guppies by 24 total fish while forgetting about the catfish. Choice C ($\frac{1}{3}$) is actually the probability that the fish IS an angelfish—a common error where students forget they're looking for the complement. Choice D ($\frac{3}{4}$) could result from miscounting the total or incorrectly calculating ratios. Remember: for "not" probability questions, you can either subtract the unwanted probability from 1, or count favorable outcomes directly. Both methods should give the same answer, so use whichever feels more natural as a way to check your work.

Question 18

1. (\frac{3}{52})
2. (\frac{3}{26}) (correct answer)
3. (\frac{3}{13})
4. (\frac{1}{2})

Explanation: A standard deck has 52 cards. There are two red suits: Hearts and Diamonds. Each suit has three face cards: Jack, Queen, and King. So, the number of red face cards is 2 suits × 3 face cards/suit = 6. These are the favorable outcomes. The total number of outcomes is 52. The probability is (\frac{6}{52}), which simplifies to (\frac{3}{26}).

Question 19

1. (\frac{5}{8}) (correct answer)
2. (\frac{3}{5})
3. (\frac{3}{8})
4. (\frac{5}{3})

Explanation: When you see a probability question, remember that probability equals the number of favorable outcomes divided by the total number of possible outcomes. Here, you want the probability of picking a fiction book at random. First, find the total number of books: 15 fiction books + 9 non-fiction books = 24 total books. Since you want a fiction book, the favorable outcomes are the 15 fiction books. Therefore, the probability is $\frac{15}{24}$. To simplify this fraction, find the greatest common factor of 15 and 24. Both numbers are divisible by 3: $\frac{15}{24} = \frac{15 ÷ 3}{24 ÷ 3} = \frac{5}{8}$. This matches answer choice A. Looking at the wrong answers: Choice B ($\frac{3}{5}$) might come from incorrectly using only the fiction and non-fiction books in some ratio, but not the correct probability calculation. Choice C ($\frac{3}{8}$) could result from using the 9 non-fiction books as your numerator instead of the 15 fiction books—this would give you the probability of selecting a non-fiction book. Choice D ($\frac{5}{3}$) is impossible since probabilities must be between 0 and 1, and this fraction is greater than 1. For probability questions, always double-check that your answer makes sense. Since there are more fiction books (15) than non-fiction books (9), the probability of selecting fiction should be greater than $\frac{1}{2}$. Only choice A meets this requirement.

Question 20

1. (\frac{3}{7})
2. (\frac{4}{9}) (correct answer)
3. (\frac{5}{9})
4. (\frac{12}{35})

Explanation: First, calculate the new number of bottles in the cooler. The number of water bottles is 20 - 5 = 15. The number of juice bottles is 15 - 3 = 12. The new total number of bottles is 15 + 12 = 27. The number of favorable outcomes (choosing a juice bottle) is 12. The probability is (\frac{12}{27}). This fraction simplifies by dividing the numerator and denominator by 3, which gives (\frac{4}{9}).