Real-World Probability - ISEE Lower Level: Mathematics Achievement
Card 1 of 24
What is the probability that a randomly chosen day of the week is a weekend day?
What is the probability that a randomly chosen day of the week is a weekend day?
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$\frac{2}{7}$. Two weekend days (Saturday, Sunday) out of seven days in a week.
$\frac{2}{7}$. Two weekend days (Saturday, Sunday) out of seven days in a week.
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What is the probability that a random integer from $1$ to $10$ is a multiple of $3$?
What is the probability that a random integer from $1$ to $10$ is a multiple of $3$?
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$\frac{3}{10}$. Three multiples of 3 (3,6,9) from integers 1 to 10.
$\frac{3}{10}$. Three multiples of 3 (3,6,9) from integers 1 to 10.
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What is the probability that a random integer from $1$ to $20$ is prime?
What is the probability that a random integer from $1$ to $20$ is prime?
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$\frac{8}{20}$. Eight primes (2,3,5,7,11,13,17,19) from integers 1 to 20.
$\frac{8}{20}$. Eight primes (2,3,5,7,11,13,17,19) from integers 1 to 20.
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What is $P(A\text{ or }B)$ if $A$ and $B$ are mutually exclusive?
What is $P(A\text{ or }B)$ if $A$ and $B$ are mutually exclusive?
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$P(A\text{ or }B)=P(A)+P(B)$. Mutually exclusive events have no overlap, so add their probabilities for the union.
$P(A\text{ or }B)=P(A)+P(B)$. Mutually exclusive events have no overlap, so add their probabilities for the union.
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What is $P(A\text{ and }B)$ if $A$ and $B$ are independent?
What is $P(A\text{ and }B)$ if $A$ and $B$ are independent?
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$P(A\text{ and }B)=P(A)\cdot P(B)$. Independent events' occurrences don't affect each other, so multiply probabilities for intersection.
$P(A\text{ and }B)=P(A)\cdot P(B)$. Independent events' occurrences don't affect each other, so multiply probabilities for intersection.
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What is the probability of rolling a $2$ or $5$ on one fair die?
What is the probability of rolling a $2$ or $5$ on one fair die?
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$\frac{1}{3}$. Two favorable outcomes (2 or 5) out of six, mutually exclusive.
$\frac{1}{3}$. Two favorable outcomes (2 or 5) out of six, mutually exclusive.
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What is the probability of flipping two heads in $2$ fair coin flips?
What is the probability of flipping two heads in $2$ fair coin flips?
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$\frac{1}{4}$. Independent flips each with probability $\frac{1}{2}$, so multiply for both heads.
$\frac{1}{4}$. Independent flips each with probability $\frac{1}{2}$, so multiply for both heads.
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What is the probability of not rolling a $6$ on one fair die?
What is the probability of not rolling a $6$ on one fair die?
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$\frac{5}{6}$. Complement of rolling a 6, which has probability $\frac{1}{6}$, subtracted from 1.
$\frac{5}{6}$. Complement of rolling a 6, which has probability $\frac{1}{6}$, subtracted from 1.
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What inequality must any probability $P(A)$ satisfy?
What inequality must any probability $P(A)$ satisfy?
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$0\le P(A)\le 1$. Probabilities range from zero for impossibility to one for certainty, inclusive.
$0\le P(A)\le 1$. Probabilities range from zero for impossibility to one for certainty, inclusive.
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What is the probability of an event that is impossible?
What is the probability of an event that is impossible?
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$0$. An impossible event has no favorable outcomes, resulting in zero probability.
$0$. An impossible event has no favorable outcomes, resulting in zero probability.
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What is the probability of an event that is certain?
What is the probability of an event that is certain?
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$1$. A certain event includes all possible outcomes, yielding probability one.
$1$. A certain event includes all possible outcomes, yielding probability one.
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What is the probability of rolling an even number on a fair die?
What is the probability of rolling an even number on a fair die?
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$\frac{1}{2}$. Three even numbers (2,4,6) out of six possible outcomes on a fair die.
$\frac{1}{2}$. Three even numbers (2,4,6) out of six possible outcomes on a fair die.
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What is $P(A)$ if $P(A^c)=0.27$?
What is $P(A)$ if $P(A^c)=0.27$?
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$0.73$. Apply the complement rule: subtract $P(A^c)$ from 1 to find $P(A)$.
$0.73$. Apply the complement rule: subtract $P(A^c)$ from 1 to find $P(A)$.
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What is the complement rule for an event $A$?
What is the complement rule for an event $A$?
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$P(A^c)=1-P(A)$. The complement covers all outcomes not in $A$, so its probability is one minus $P(A)$.
$P(A^c)=1-P(A)$. The complement covers all outcomes not in $A$, so its probability is one minus $P(A)$.
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What is the formula for probability when outcomes are equally likely?
What is the formula for probability when outcomes are equally likely?
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$P(A)=\frac{\text{favorable outcomes}}{\text{total outcomes}}$. When all outcomes are equally likely, probability is the ratio of favorable to total outcomes.
$P(A)=\frac{\text{favorable outcomes}}{\text{total outcomes}}$. When all outcomes are equally likely, probability is the ratio of favorable to total outcomes.
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What is the probability of rolling a $6$ on a fair six-sided die?
What is the probability of rolling a $6$ on a fair six-sided die?
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$\frac{1}{6}$. One favorable outcome out of six equally likely die faces.
$\frac{1}{6}$. One favorable outcome out of six equally likely die faces.
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What is the probability of flipping at least one head in $2$ fair coin flips?
What is the probability of flipping at least one head in $2$ fair coin flips?
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$\frac{3}{4}$. Out of four possible outcomes in two flips, three include at least one head.
$\frac{3}{4}$. Out of four possible outcomes in two flips, three include at least one head.
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What is the probability of drawing a red card from a standard $52$-card deck?
What is the probability of drawing a red card from a standard $52$-card deck?
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$\frac{1}{2}$. Standard deck has 26 red cards out of 52 total cards.
$\frac{1}{2}$. Standard deck has 26 red cards out of 52 total cards.
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What is the probability of drawing an ace from a standard $52$-card deck?
What is the probability of drawing an ace from a standard $52$-card deck?
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$\frac{1}{13}$. Four aces in a 52-card deck simplify to this fraction.
$\frac{1}{13}$. Four aces in a 52-card deck simplify to this fraction.
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What is the probability of drawing a heart from a standard $52$-card deck?
What is the probability of drawing a heart from a standard $52$-card deck?
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$\frac{1}{4}$. Thirteen hearts out of 52 cards in a standard deck.
$\frac{1}{4}$. Thirteen hearts out of 52 cards in a standard deck.
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What is the probability of choosing a blue marble from $3$ blue and $5$ green marbles?
What is the probability of choosing a blue marble from $3$ blue and $5$ green marbles?
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$\frac{3}{8}$. Three blue marbles out of eight total marbles.
$\frac{3}{8}$. Three blue marbles out of eight total marbles.
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What is the probability of choosing a green marble from $3$ blue and $5$ green marbles?
What is the probability of choosing a green marble from $3$ blue and $5$ green marbles?
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$\frac{5}{8}$. Five green marbles out of eight total marbles.
$\frac{5}{8}$. Five green marbles out of eight total marbles.
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What is the probability of choosing a vowel from the letters in the word $\text{MATH}$?
What is the probability of choosing a vowel from the letters in the word $\text{MATH}$?
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$\frac{1}{4}$. One vowel (A) among the four letters M, A, T, H.
$\frac{1}{4}$. One vowel (A) among the four letters M, A, T, H.
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What is the probability that a randomly chosen month has $31$ days?
What is the probability that a randomly chosen month has $31$ days?
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$\frac{7}{12}$. Seven months (Jan, Mar, May, Jul, Aug, Oct, Dec) have 31 days out of 12.
$\frac{7}{12}$. Seven months (Jan, Mar, May, Jul, Aug, Oct, Dec) have 31 days out of 12.
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