Comparing Probabilities - ISEE Middle Level: Mathematics Achievement
Card 1 of 22
Which probability is closest to $1$: $\frac{7}{8}$, $\frac{5}{6}$, or $\frac{9}{10}$?
Which probability is closest to $1$: $\frac{7}{8}$, $\frac{5}{6}$, or $\frac{9}{10}$?
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$\frac{9}{10}$. $\frac{9}{10}=0.9$ is nearest to $1$, compared to $\frac{7}{8}=0.875$ and $\frac{5}{6} \approx 0.833$.
$\frac{9}{10}$. $\frac{9}{10}=0.9$ is nearest to $1$, compared to $\frac{7}{8}=0.875$ and $\frac{5}{6} \approx 0.833$.
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Which is more likely: $3$ heads in $3$ fair coin flips or $0$ heads in $3$ flips?
Which is more likely: $3$ heads in $3$ fair coin flips or $0$ heads in $3$ flips?
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They are equally likely. Both outcomes have probability $\frac{1}{8}$ in a binomial distribution with fair coins.
They are equally likely. Both outcomes have probability $\frac{1}{8}$ in a binomial distribution with fair coins.
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Which probability is larger: $\frac{9}{25}$ or $35%$?
Which probability is larger: $\frac{9}{25}$ or $35%$?
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$\frac{9}{25}$. Converting shows $\frac{9}{25}=0.36$ exceeds $35%=0.35$.
$\frac{9}{25}$. Converting shows $\frac{9}{25}=0.36$ exceeds $35%=0.35$.
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Which probability is larger: $P(E)$ or $P(E^c)$ if $P(E)=0.6$?
Which probability is larger: $P(E)$ or $P(E^c)$ if $P(E)=0.6$?
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$P(E)$. With $P(E)=0.6$, it exceeds $P(E^c)=0.4$.
$P(E)$. With $P(E)=0.6$, it exceeds $P(E^c)=0.4$.
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Which probability is larger: $45%$ or $0.43$?
Which probability is larger: $45%$ or $0.43$?
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$45%$. Converting $45%$ to $0.45$ shows it exceeds $0.43$.
$45%$. Converting $45%$ to $0.45$ shows it exceeds $0.43$.
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What is the probability of an event $E$ in terms of favorable and total outcomes?
What is the probability of an event $E$ in terms of favorable and total outcomes?
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$P(E)=\frac{\text{favorable}}{\text{total}}$. Probability measures the likelihood as the ratio of favorable outcomes to total possible outcomes in a uniform sample space.
$P(E)=\frac{\text{favorable}}{\text{total}}$. Probability measures the likelihood as the ratio of favorable outcomes to total possible outcomes in a uniform sample space.
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Which probability is larger: $\frac{3}{8}$ or $\frac{2}{5}$?
Which probability is larger: $\frac{3}{8}$ or $\frac{2}{5}$?
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$\frac{2}{5}$. Converting to decimals shows $\frac{2}{5}=0.4$ exceeds $\frac{3}{8}=0.375$.
$\frac{2}{5}$. Converting to decimals shows $\frac{2}{5}=0.4$ exceeds $\frac{3}{8}=0.375$.
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Which probability is larger: $\frac{5}{12}$ or $\frac{2}{3}$?
Which probability is larger: $\frac{5}{12}$ or $\frac{2}{3}$?
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$\frac{2}{3}$. Converting to decimals reveals $\frac{2}{3} \approx 0.667$ is greater than $\frac{5}{12} \approx 0.417$.
$\frac{2}{3}$. Converting to decimals reveals $\frac{2}{3} \approx 0.667$ is greater than $\frac{5}{12} \approx 0.417$.
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Which probability is larger: $\frac{7}{20}$ or $0.36$?
Which probability is larger: $\frac{7}{20}$ or $0.36$?
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$0.36$. $0.36$ is greater than $\frac{7}{20}=0.35$ when compared as decimals.
$0.36$. $0.36$ is greater than $\frac{7}{20}=0.35$ when compared as decimals.
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Which probability is larger: $0.37$ or $\frac{3}{10}$?
Which probability is larger: $0.37$ or $\frac{3}{10}$?
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$0.37$. $0.37$ exceeds $\frac{3}{10}=0.3$ when compared directly as decimals.
$0.37$. $0.37$ exceeds $\frac{3}{10}=0.3$ when compared directly as decimals.
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Which probability is larger: $0.125$ or $\frac{1}{9}$?
Which probability is larger: $0.125$ or $\frac{1}{9}$?
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$0.125$. $0.125$ exceeds $\frac{1}{9} \approx 0.111$ when compared as decimals.
$0.125$. $0.125$ exceeds $\frac{1}{9} \approx 0.111$ when compared as decimals.
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Which probability is larger: $\frac{3}{7}$ or $\frac{4}{9}$?
Which probability is larger: $\frac{3}{7}$ or $\frac{4}{9}$?
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$\frac{4}{9}$. Converting to decimals reveals $\frac{4}{9} \approx 0.444$ is greater than $\frac{3}{7} \approx 0.429$.
$\frac{4}{9}$. Converting to decimals reveals $\frac{4}{9} \approx 0.444$ is greater than $\frac{3}{7} \approx 0.429$.
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Which is more likely: rolling an even number or rolling a number greater than $4$ on a fair die?
Which is more likely: rolling an even number or rolling a number greater than $4$ on a fair die?
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Rolling an even number. Even numbers (2,4,6) have probability $\frac{3}{6}=0.5$, exceeding numbers greater than 4 (5,6) at $\frac{2}{6} \approx 0.333$.
Rolling an even number. Even numbers (2,4,6) have probability $\frac{3}{6}=0.5$, exceeding numbers greater than 4 (5,6) at $\frac{2}{6} \approx 0.333$.
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Which probability is larger: $\frac{5}{8}$ or $62%$?
Which probability is larger: $\frac{5}{8}$ or $62%$?
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$\frac{5}{8}$. Converting shows $\frac{5}{8}=0.625$ exceeds $62%=0.62$.
$\frac{5}{8}$. Converting shows $\frac{5}{8}=0.625$ exceeds $62%=0.62$.
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Which probability is larger: $\frac{13}{50}$ or $0.27$?
Which probability is larger: $\frac{13}{50}$ or $0.27$?
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$0.27$. $0.27$ is greater than $\frac{13}{50}=0.26$ in decimal form.
$0.27$. $0.27$ is greater than $\frac{13}{50}=0.26$ in decimal form.
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Which probability is larger: $\frac{4}{9}$ or $0.45$?
Which probability is larger: $\frac{4}{9}$ or $0.45$?
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$0.45$. $0.45$ slightly exceeds $\frac{4}{9} \approx 0.444$ when compared as decimals.
$0.45$. $0.45$ slightly exceeds $\frac{4}{9} \approx 0.444$ when compared as decimals.
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Which probability is larger: $\frac{11}{30}$ or $\frac{3}{8}$?
Which probability is larger: $\frac{11}{30}$ or $\frac{3}{8}$?
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$\frac{3}{8}$. Converting to decimals indicates $\frac{3}{8}=0.375$ is greater than $\frac{11}{30} \approx 0.367$.
$\frac{3}{8}$. Converting to decimals indicates $\frac{3}{8}=0.375$ is greater than $\frac{11}{30} \approx 0.367$.
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Which probability is larger: $\frac{17}{40}$ or $0.41$?
Which probability is larger: $\frac{17}{40}$ or $0.41$?
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$\frac{17}{40}$. Converting shows $\frac{17}{40}=0.425$ exceeds $0.41$.
$\frac{17}{40}$. Converting shows $\frac{17}{40}=0.425$ exceeds $0.41$.
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Which probability is closest to $\frac{1}{2}$: $0.49$, $0.52$, or $0.6$?
Which probability is closest to $\frac{1}{2}$: $0.49$, $0.52$, or $0.6$?
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$0.49$. $0.49$ is closest to $0.5$, being only $0.01$ away compared to $0.02$ for $0.52$ and $0.1$ for $0.6$.
$0.49$. $0.49$ is closest to $0.5$, being only $0.01$ away compared to $0.02$ for $0.52$ and $0.1$ for $0.6$.
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Which probability is larger: $\frac{1}{4}$ or $0.26$?
Which probability is larger: $\frac{1}{4}$ or $0.26$?
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$0.26$. $0.26$ exceeds $\frac{1}{4}=0.25$ when compared directly.
$0.26$. $0.26$ exceeds $\frac{1}{4}=0.25$ when compared directly.
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What is the complement rule for an event $E$?
What is the complement rule for an event $E$?
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$P(E^c)=1-P(E)$. The complement rule states that the probability of an event not occurring is one minus the probability of it occurring.
$P(E^c)=1-P(E)$. The complement rule states that the probability of an event not occurring is one minus the probability of it occurring.
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Which probability is larger: $P(E)$ or $P(E^c)$ if $P(E)=\frac{2}{5}$?
Which probability is larger: $P(E)$ or $P(E^c)$ if $P(E)=\frac{2}{5}$?
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$P(E^c)$. Given $P(E)=\frac{2}{5}=0.4$, $P(E^c)=0.6$ is larger.
$P(E^c)$. Given $P(E)=\frac{2}{5}=0.4$, $P(E^c)=0.6$ is larger.
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