Calculating Probability - ISEE Lower Level: Quantitative Reasoning
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What is the probability of flipping heads on a fair coin?
What is the probability of flipping heads on a fair coin?
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$\frac{1}{2}$. A fair coin has two equally likely outcomes, heads and tails, so the probability of heads is one out of two.
$\frac{1}{2}$. A fair coin has two equally likely outcomes, heads and tails, so the probability of heads is one out of two.
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What is the probability formula for the complement of event $E$?
What is the probability formula for the complement of event $E$?
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$P(E^c)=1-P(E)$. The probability of the complement event $E^c$ is one minus the probability of $E$, as they are mutually exclusive and exhaustive.
$P(E^c)=1-P(E)$. The probability of the complement event $E^c$ is one minus the probability of $E$, as they are mutually exclusive and exhaustive.
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If $P(E)=\frac{2}{5}$, what is $P(E^c)$?
If $P(E)=\frac{2}{5}$, what is $P(E^c)$?
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$\frac{3}{5}$. The complement probability is found by subtracting $P(E)$ from 1.
$\frac{3}{5}$. The complement probability is found by subtracting $P(E)$ from 1.
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A bag has $5$ green, $4$ yellow, and $1$ purple marble. What is $P(\text{yellow})$?
A bag has $5$ green, $4$ yellow, and $1$ purple marble. What is $P(\text{yellow})$?
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$\frac{2}{5}$. With 4 yellow out of 10 total marbles, the probability simplifies to this fraction assuming equal likelihood.
$\frac{2}{5}$. With 4 yellow out of 10 total marbles, the probability simplifies to this fraction assuming equal likelihood.
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A class has $18$ students: $10$ wear glasses. What is $P(\text{glasses})$ in simplest form?
A class has $18$ students: $10$ wear glasses. What is $P(\text{glasses})$ in simplest form?
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$\frac{5}{9}$. Simplify the ratio of students with glasses to total students by dividing numerator and denominator by 2.
$\frac{5}{9}$. Simplify the ratio of students with glasses to total students by dividing numerator and denominator by 2.
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What is the probability of choosing a red marble if there are $3$ red and $7$ blue marbles?
What is the probability of choosing a red marble if there are $3$ red and $7$ blue marbles?
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$\frac{3}{10}$. The probability is the ratio of red marbles to the total marbles, assuming each marble is equally likely to be chosen.
$\frac{3}{10}$. The probability is the ratio of red marbles to the total marbles, assuming each marble is equally likely to be chosen.
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What is the probability of choosing a blue marble if there are $3$ red and $7$ blue marbles?
What is the probability of choosing a blue marble if there are $3$ red and $7$ blue marbles?
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$\frac{7}{10}$. The probability is the ratio of blue marbles to the total marbles, assuming each marble is equally likely to be chosen.
$\frac{7}{10}$. The probability is the ratio of blue marbles to the total marbles, assuming each marble is equally likely to be chosen.
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What is the probability of rolling a $6$ on a fair six-sided number cube?
What is the probability of rolling a $6$ on a fair six-sided number cube?
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$\frac{1}{6}$. Each face of the die is equally likely, so the probability is one favorable outcome divided by six total outcomes.
$\frac{1}{6}$. Each face of the die is equally likely, so the probability is one favorable outcome divided by six total outcomes.
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What is the probability of rolling an even number on a fair six-sided number cube?
What is the probability of rolling an even number on a fair six-sided number cube?
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$\frac{1}{2}$. Three even numbers (2, 4, 6) out of six possible outcomes on the die yield this probability.
$\frac{1}{2}$. Three even numbers (2, 4, 6) out of six possible outcomes on the die yield this probability.
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What is the probability of rolling a number greater than $4$ on a fair six-sided number cube?
What is the probability of rolling a number greater than $4$ on a fair six-sided number cube?
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$\frac{1}{3}$. Two numbers greater than 4 (5 and 6) out of six possible outcomes on the die yield this probability.
$\frac{1}{3}$. Two numbers greater than 4 (5 and 6) out of six possible outcomes on the die yield this probability.
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What is the probability of flipping heads twice in $2$ fair coin flips?
What is the probability of flipping heads twice in $2$ fair coin flips?
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$\frac{1}{4}$. The probability of heads on each independent flip is $\frac{1}{2}$, so for two heads it is $\left(\frac{1}{2}\right)^2$.
$\frac{1}{4}$. The probability of heads on each independent flip is $\frac{1}{2}$, so for two heads it is $\left(\frac{1}{2}\right)^2$.
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A bag has $5$ green, $4$ yellow, and $1$ purple marble. What is $P(\text{not green})$?
A bag has $5$ green, $4$ yellow, and $1$ purple marble. What is $P(\text{not green})$?
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$\frac{1}{2}$. This is the complement of drawing a green marble, or equivalently the ratio of non-green marbles to total marbles.
$\frac{1}{2}$. This is the complement of drawing a green marble, or equivalently the ratio of non-green marbles to total marbles.
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A jar has $12$ candies: $5$ are lemon. What is $P(\text{lemon})$ in simplest form?
A jar has $12$ candies: $5$ are lemon. What is $P(\text{lemon})$ in simplest form?
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$\frac{5}{12}$. The probability is the ratio of lemon candies to total candies, already in simplest form.
$\frac{5}{12}$. The probability is the ratio of lemon candies to total candies, already in simplest form.
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A spinner has $8$ equal sections, and $3$ are shaded. What is $P(\text{shaded})$?
A spinner has $8$ equal sections, and $3$ are shaded. What is $P(\text{shaded})$?
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$\frac{3}{8}$. Each section is equally likely, so the probability is the number of shaded sections divided by total sections.
$\frac{3}{8}$. Each section is equally likely, so the probability is the number of shaded sections divided by total sections.
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A ratio of favorable to total outcomes is $9:12$. What is the probability in simplest form?
A ratio of favorable to total outcomes is $9:12$. What is the probability in simplest form?
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$\frac{3}{4}$. Simplify the ratio 9:12 by dividing both parts by 3 to get the probability as a fraction.
$\frac{3}{4}$. Simplify the ratio 9:12 by dividing both parts by 3 to get the probability as a fraction.
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A box has $6$ red, $2$ blue, and $4$ white balls. What is $P(\text{red or blue})$?
A box has $6$ red, $2$ blue, and $4$ white balls. What is $P(\text{red or blue})$?
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$\frac{2}{3}$. Add red and blue balls for favorable outcomes, then divide by total balls to get the probability.
$\frac{2}{3}$. Add red and blue balls for favorable outcomes, then divide by total balls to get the probability.
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A box has $6$ red, $2$ blue, and $4$ white balls. What is $P(\text{not white})$?
A box has $6$ red, $2$ blue, and $4$ white balls. What is $P(\text{not white})$?
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$\frac{2}{3}$. This is the complement of drawing a white ball, calculated as 1 minus the probability of white.
$\frac{2}{3}$. This is the complement of drawing a white ball, calculated as 1 minus the probability of white.
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If $P(E)=\frac{1}{8}$, what is $P(E)$ as a percent?
If $P(E)=\frac{1}{8}$, what is $P(E)$ as a percent?
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$12.5%$. Convert the fraction $\frac{1}{8}$ to a decimal 0.125 and then to a percent by multiplying by 100.
$12.5%$. Convert the fraction $\frac{1}{8}$ to a decimal 0.125 and then to a percent by multiplying by 100.
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If $P(E)=\frac{3}{4}$, what is $P(E)$ as a decimal?
If $P(E)=\frac{3}{4}$, what is $P(E)$ as a decimal?
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$0.75$. Divide the numerator 3 by the denominator 4 to express the probability as a decimal.
$0.75$. Divide the numerator 3 by the denominator 4 to express the probability as a decimal.
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A drawer has $9$ socks: $4$ black and $5$ white. What is $P(\text{black})$?
A drawer has $9$ socks: $4$ black and $5$ white. What is $P(\text{black})$?
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$\frac{4}{9}$. The probability is the ratio of black socks to total socks, assuming each sock is equally likely to be drawn.
$\frac{4}{9}$. The probability is the ratio of black socks to total socks, assuming each sock is equally likely to be drawn.
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A deck has $52$ cards. What is the probability of drawing a heart?
A deck has $52$ cards. What is the probability of drawing a heart?
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$\frac{1}{4}$. There are 13 hearts in a standard deck of 52 cards, so the probability simplifies to this fraction.
$\frac{1}{4}$. There are 13 hearts in a standard deck of 52 cards, so the probability simplifies to this fraction.
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