ISEE Middle Level Mathematics Achievement Flashcards: Comparing Probabilities

What this deck covers

This deck focuses on Comparing Probabilities, giving you a quick way to review the definitions, rules, and examples that matter most for ISEE Middle Level Mathematics Achievement.

How to use these flashcards

Work through these flashcards in short sessions. Try to answer each prompt before flipping the card, then revisit any cards you miss until the explanation feels automatic.

Flashcard 1: Which probability is larger: $\frac{9}{25}$ or $35\%$?

Answer: $\frac{9}{25}$. Converting shows $\frac{9}{25}=0.36$ exceeds $35\%=0.35$.

Flashcard 2: Which probability is larger: $P(E)$ or $P(E^c)$ if $P(E)=0.6$?

Answer: $P(E)$. With $P(E)=0.6$, it exceeds $P(E^c)=0.4$.

Flashcard 3: Which is more likely: rolling an even number or rolling a number greater than $4$ on a fair die?

Answer: Rolling an even number. Even numbers (2,4,6) have probability $\frac{3}{6}=0.5$, exceeding numbers greater than 4 (5,6) at $\frac{2}{6} \approx 0.333$.

Flashcard 4: Which probability is larger: $\frac{13}{50}$ or $0.27$?

Answer: $0.27$. $0.27$ is greater than $\frac{13}{50}=0.26$ in decimal form.

Flashcard 5: Which probability is larger: $0.37$ or $\frac{3}{10}$?

Answer: $0.37$. $0.37$ exceeds $\frac{3}{10}=0.3$ when compared directly as decimals.

Flashcard 6: Which probability is larger: $\frac{11}{30}$ or $\frac{3}{8}$?

Answer: $\frac{3}{8}$. Converting to decimals indicates $\frac{3}{8}=0.375$ is greater than $\frac{11}{30} \approx 0.367$.

Flashcard 7: What is the probability of an event $E$ in terms of favorable and total outcomes?

Answer: $P(E)=\frac{\text{favorable}}{\text{total}}$. Probability measures the likelihood as the ratio of favorable outcomes to total possible outcomes in a uniform sample space.

Flashcard 8: Which probability is larger: $\frac{4}{9}$ or $0.45$?

Answer: $0.45$. $0.45$ slightly exceeds $\frac{4}{9} \approx 0.444$ when compared as decimals.

Flashcard 9: Which probability is larger: $\frac{1}{4}$ or $0.26$?

Answer: $0.26$. $0.26$ exceeds $\frac{1}{4}=0.25$ when compared directly.

Flashcard 10: Which probability is larger: $P(E)$ or $P(E^c)$ if $P(E)=\frac{2}{5}$?

Answer: $P(E^c)$. Given $P(E)=\frac{2}{5}=0.4$, $P(E^c)=0.6$ is larger.

Flashcard 11: Which probability is larger: $\frac{3}{8}$ or $\frac{2}{5}$?

Answer: $\frac{2}{5}$. Converting to decimals shows $\frac{2}{5}=0.4$ exceeds $\frac{3}{8}=0.375$.

Flashcard 12: Which probability is closest to $\frac{1}{2}$: $0.49$, $0.52$, or $0.6$?

Answer: $0.49$. $0.49$ is closest to $0.5$, being only $0.01$ away compared to $0.02$ for $0.52$ and $0.1$ for $0.6$.

Flashcard 13: Which probability is larger: $\frac{5}{8}$ or $62\%$?

Answer: $\frac{5}{8}$. Converting shows $\frac{5}{8}=0.625$ exceeds $62\%=0.62$.

Flashcard 14: Which probability is larger: $\frac{3}{7}$ or $\frac{4}{9}$?

Answer: $\frac{4}{9}$. Converting to decimals reveals $\frac{4}{9} \approx 0.444$ is greater than $\frac{3}{7} \approx 0.429$.

Flashcard 15: Which probability is larger: $\frac{7}{20}$ or $0.36$?

Answer: $0.36$. $0.36$ is greater than $\frac{7}{20}=0.35$ when compared as decimals.

Flashcard 16: What is the complement rule for an event $E$?

Answer: $P(E^c)=1-P(E)$. The complement rule states that the probability of an event not occurring is one minus the probability of it occurring.

Flashcard 17: Which probability is larger: $\frac{17}{40}$ or $0.41$?

Answer: $\frac{17}{40}$. Converting shows $\frac{17}{40}=0.425$ exceeds $0.41$.

Flashcard 18: Which probability is larger: $\frac{5}{12}$ or $\frac{2}{3}$?

Answer: $\frac{2}{3}$. Converting to decimals reveals $\frac{2}{3} \approx 0.667$ is greater than $\frac{5}{12} \approx 0.417$.

Flashcard 19: Which probability is larger: $0.125$ or $\frac{1}{9}$?

Answer: $0.125$. $0.125$ exceeds $\frac{1}{9} \approx 0.111$ when compared as decimals.

Flashcard 20: Which probability is larger: $45\%$ or $0.43$?

Answer: $45\%$. Converting $45\%$ to $0.45$ shows it exceeds $0.43$.

Flashcard 21: Which is more likely: $3$ heads in $3$ fair coin flips or $0$ heads in $3$ flips?

Answer: They are equally likely. Both outcomes have probability $\frac{1}{8}$ in a binomial distribution with fair coins.

Flashcard 22: Which probability is closest to $1$: $\frac{7}{8}$, $\frac{5}{6}$, or $\frac{9}{10}$?

Answer: $\frac{9}{10}$. $\frac{9}{10}=0.9$ is nearest to $1$, compared to $\frac{7}{8}=0.875$ and $\frac{5}{6} \approx 0.833$.