Understand Compound Event Probability - 7th Grade Math
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Which sample space size is correct for rolling one fair six-sided die once?
Which sample space size is correct for rolling one fair six-sided die once?
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$6$. A standard die has faces numbered $1$ through $6$.
$6$. A standard die has faces numbered $1$ through $6$.
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What is $P(\text{sum }\le 3)$ when rolling two fair six-sided dice?
What is $P(\text{sum }\le 3)$ when rolling two fair six-sided dice?
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$\frac{3}{36}$. Only $(1,1), (1,2), (2,1)$ give sums $\le 3$ out of $36$ outcomes.
$\frac{3}{36}$. Only $(1,1), (1,2), (2,1)$ give sums $\le 3$ out of $36$ outcomes.
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What is $P(\text{sum }=7)$ when rolling two fair six-sided dice?
What is $P(\text{sum }=7)$ when rolling two fair six-sided dice?
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$\frac{6}{36}$. Six ways to get sum $7$: $(1,6), (2,5), (3,4), (4,3), (5,2), (6,1)$.
$\frac{6}{36}$. Six ways to get sum $7$: $(1,6), (2,5), (3,4), (4,3), (5,2), (6,1)$.
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Identify the correct probability: choosing a heart from a standard $52$-card deck.
Identify the correct probability: choosing a heart from a standard $52$-card deck.
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$\frac{1}{4}$. There are $13$ hearts in $52$ cards, so $\frac{13}{52} = \frac{1}{4}$.
$\frac{1}{4}$. There are $13$ hearts in $52$ cards, so $\frac{13}{52} = \frac{1}{4}$.
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What is the sample space size for flipping a fair coin and rolling a fair die?
What is the sample space size for flipping a fair coin and rolling a fair die?
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$12$. Coin has $2$ outcomes, die has $6$, so $2 \times 6 = 12$ total.
$12$. Coin has $2$ outcomes, die has $6$, so $2 \times 6 = 12$ total.
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What does the sample space represent for a probability experiment?
What does the sample space represent for a probability experiment?
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The set of all possible outcomes. Contains every outcome that could happen in an experiment.
The set of all possible outcomes. Contains every outcome that could happen in an experiment.
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What is a compound event in probability?
What is a compound event in probability?
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An event made of two or more simple events. Combines multiple simple events like "heads AND tails" or "red OR blue".
An event made of two or more simple events. Combines multiple simple events like "heads AND tails" or "red OR blue".
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What is the definition of probability using a sample space?
What is the definition of probability using a sample space?
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$P(E)=\frac{\text{number of outcomes in }E}{\text{total outcomes in sample space}}$. Probability equals favorable outcomes divided by total outcomes.
$P(E)=\frac{\text{number of outcomes in }E}{\text{total outcomes in sample space}}$. Probability equals favorable outcomes divided by total outcomes.
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What is $P(\text{at least one head})$ for two fair coin flips?
What is $P(\text{at least one head})$ for two fair coin flips?
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$\frac{3}{4}$. Three favorable outcomes: $HH, HT, TH$ out of four total.
$\frac{3}{4}$. Three favorable outcomes: $HH, HT, TH$ out of four total.
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What is $P(\text{both heads})$ for two fair coin flips?
What is $P(\text{both heads})$ for two fair coin flips?
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$\frac{1}{4}$. Only one outcome $HH$ out of four possible: ${HH, HT, TH, TT}$.
$\frac{1}{4}$. Only one outcome $HH$ out of four possible: ${HH, HT, TH, TT}$.
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What is $P(\text{exactly one head})$ for two fair coin flips?
What is $P(\text{exactly one head})$ for two fair coin flips?
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$\frac{2}{4}$. Two outcomes have exactly one head: $HT$ and $TH$.
$\frac{2}{4}$. Two outcomes have exactly one head: $HT$ and $TH$.
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What is the sample space size for two fair coin flips?
What is the sample space size for two fair coin flips?
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$4$. Two flips give outcomes: ${HH, HT, TH, TT}$.
$4$. Two flips give outcomes: ${HH, HT, TH, TT}$.
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Identify the probability: pick a number from ${1,2,3,4,5}$, $P(\text{odd or }5)$.
Identify the probability: pick a number from ${1,2,3,4,5}$, $P(\text{odd or }5)$.
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$\frac{3}{5}$. Odd numbers are ${1,3,5}$, which includes $5$, so $3$ favorable outcomes.
$\frac{3}{5}$. Odd numbers are ${1,3,5}$, which includes $5$, so $3$ favorable outcomes.
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What is $P(\text{red or face card})$ from a standard $52$-card deck?
What is $P(\text{red or face card})$ from a standard $52$-card deck?
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$\frac{32}{52}$. $26$ red cards plus $12$ face cards minus $6$ red face cards.
$\frac{32}{52}$. $26$ red cards plus $12$ face cards minus $6$ red face cards.
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What is $P(\text{red and face card})$ from a standard $52$-card deck?
What is $P(\text{red and face card})$ from a standard $52$-card deck?
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$\frac{6}{52}$. Red face cards are $6$ total: $3$ red jacks, queens, and kings.
$\frac{6}{52}$. Red face cards are $6$ total: $3$ red jacks, queens, and kings.
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What is $P(\text{not a heart})$ when drawing one card from a standard $52$-card deck?
What is $P(\text{not a heart})$ when drawing one card from a standard $52$-card deck?
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$\frac{39}{52}$. $52 - 13 = 39$ cards are not hearts.
$\frac{39}{52}$. $52 - 13 = 39$ cards are not hearts.
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What is $P(\text{even and }\gt 3)$ when rolling one fair six-sided die?
What is $P(\text{even and }\gt 3)$ when rolling one fair six-sided die?
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$\frac{2}{6}$. Even numbers $>3$ are ${4, 6}$, so $2$ favorable outcomes.
$\frac{2}{6}$. Even numbers $>3$ are ${4, 6}$, so $2$ favorable outcomes.
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A spinner has $4$ equal sections labeled $A,B,C,D$. What is $P(A\text{ or }B)$?
A spinner has $4$ equal sections labeled $A,B,C,D$. What is $P(A\text{ or }B)$?
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$\frac{2}{4}$. Two favorable sections out of four equal sections.
$\frac{2}{4}$. Two favorable sections out of four equal sections.
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A bag has $3$ red and $2$ blue marbles. Draw one marble. What is $P(\text{red})$?
A bag has $3$ red and $2$ blue marbles. Draw one marble. What is $P(\text{red})$?
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$\frac{3}{5}$. Three red marbles out of five total marbles.
$\frac{3}{5}$. Three red marbles out of five total marbles.
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A bag has $3$ red and $2$ blue marbles. Draw one marble. What is $P(\text{blue})$?
A bag has $3$ red and $2$ blue marbles. Draw one marble. What is $P(\text{blue})$?
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$\frac{2}{5}$. Two blue marbles out of five total marbles.
$\frac{2}{5}$. Two blue marbles out of five total marbles.
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What is $P(\text{at least one head})$ when flipping $2$ fair coins?
What is $P(\text{at least one head})$ when flipping $2$ fair coins?
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$\frac{3}{4}$. 3 outcomes have at least one H: (H,H),(H,T),(T,H) out of 4.
$\frac{3}{4}$. 3 outcomes have at least one H: (H,H),(H,T),(T,H) out of 4.
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What is a compound event in probability?
What is a compound event in probability?
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An event made from two or more simple events. Combines multiple simple events like "heads AND tails".
An event made from two or more simple events. Combines multiple simple events like "heads AND tails".
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Identify the sample space size for rolling one fair six-sided die.
Identify the sample space size for rolling one fair six-sided die.
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$6$. A die has 6 faces, so 6 possible outcomes.
$6$. A die has 6 faces, so 6 possible outcomes.
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What is the sample space of an experiment?
What is the sample space of an experiment?
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The set of all possible outcomes. Sample space contains every outcome that could occur.
The set of all possible outcomes. Sample space contains every outcome that could occur.
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What is the probability of an event written as a fraction of the sample space?
What is the probability of an event written as a fraction of the sample space?
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$P(E)=\frac{\text{number of favorable outcomes}}{\text{total outcomes in the sample space}}$. Favorable outcomes divided by total possible outcomes gives probability.
$P(E)=\frac{\text{number of favorable outcomes}}{\text{total outcomes in the sample space}}$. Favorable outcomes divided by total possible outcomes gives probability.
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