ISEE Middle Level Mathematics Achievement Flashcards: Calculating Probability

What this deck covers

This deck focuses on Calculating Probability, 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: What is the probability of choosing a vowel from the letters in $\text{MATH}$?

Answer: $\frac{1}{4}$. The word MATH has four distinct letters, with one vowel (A) equally likely to be chosen.

Flashcard 2: What is the probability of choosing a multiple of $3$ from $\{1,2,3,4,5,6,7,8,9\}$?

Answer: $\frac{1}{3}$. The set has nine numbers, with three multiples of 3 (3, 6, 9) equally likely to be chosen.

Flashcard 3: What is the probability of rolling a $5$ on a fair six-sided die?

Answer: $\frac{1}{6}$. A fair die has six equally likely outcomes, with only one favorable for rolling a 5.

Flashcard 4: What is the probability of getting at least one head in two fair coin flips?

Answer: $\frac{3}{4}$. Two coin flips yield four equally likely outcomes, with at least one head in three of them (HH, HT, TH).

Flashcard 5: What is the probability of drawing an ace from a standard $52$-card deck?

Answer: $\frac{1}{13}$. A standard deck has 52 cards, with 4 aces equally likely to be drawn.

Flashcard 6: What is the probability of drawing a heart from a standard $52$-card deck?

Answer: $\frac{1}{4}$. A standard deck has 52 cards, with 13 hearts equally likely to be drawn.

Flashcard 7: What is the multiplication rule for independent events $A$ and $B$?

Answer: $P(A\cap B)=P(A)\cdot P(B)$. For independent events, the joint probability multiplies individual probabilities as one does not affect the other.

Flashcard 8: What is $P(A^c)$ if $P(A)=\frac{2}{5}$?

Answer: $\frac{3}{5}$. The complement rule gives $1 - \frac{2}{5} = \frac{3}{5}$ for the probability of not $A$.

Flashcard 9: What is the probability of a certain event?

Answer: $1$. A certain event includes all possible outcomes, equaling the total probability of 1.

Flashcard 10: What is the probability of an impossible event?

Answer: $0$. An impossible event has no favorable outcomes, resulting in zero probability.

Flashcard 11: What is the probability of rolling a number greater than $4$ on a fair die?

Answer: $\frac{1}{3}$. Numbers greater than 4 (5, 6) are two of the six equally likely outcomes on a fair die.

Flashcard 12: What is $P(A\cup B)$ if $P(A)=\frac{1}{2}$, $P(B)=\frac{1}{3}$, and $P(A\cap B)=\frac{1}{6}$?

Answer: $\frac{2}{3}$. Use the general addition rule: $\frac{1}{2} + \frac{1}{3} - \frac{1}{6} = \frac{3}{6} + \frac{2}{6} - \frac{1}{6} = \frac{4}{6}$.

Flashcard 13: What is the probability of choosing a prime number from $\{1,2,3,4,5,6,7,8,9,10\}$?

Answer: $\frac{2}{5}$. The set has ten numbers, with four primes (2, 3, 5, 7) equally likely to be chosen.

Flashcard 14: What is the addition rule for any events $A$ and $B$ (may overlap)?

Answer: $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. The general addition rule subtracts the intersection to correct for overlapping outcomes in the union.

Flashcard 15: What is the addition rule for mutually exclusive events $A$ and $B$?

Answer: $P(A\cup B)=P(A)+P(B)$. For mutually exclusive events, the union probability is the sum since there is no overlap.

Flashcard 16: What is the probability of drawing a face card (J, Q, or K) from a $52$-card deck?

Answer: $\frac{3}{13}$. A standard deck has 52 cards, with 12 face cards (J, Q, K in 4 suits) equally likely to be drawn.

Flashcard 17: What is the probability of getting heads on a fair coin?

Answer: $\frac{1}{2}$. A fair coin has two equally likely outcomes, with heads as one of them.

Flashcard 18: What is the probability of rolling an even number on a fair die?

Answer: $\frac{1}{2}$. Even numbers (2, 4, 6) are three of the six equally likely outcomes on a fair die.

Flashcard 19: What is the probability of getting two heads in two fair coin flips?

Answer: $\frac{1}{4}$. Two coin flips yield four equally likely outcomes, with two heads (HH) in one of them.

Flashcard 20: What is the complement rule for an event $A$?

Answer: $P(A^c)=1-P(A)$. The complement rule subtracts the probability of event $A$ from 1 to find the probability of not $A$.

Flashcard 21: What is $P(A\cap B)$ if $P(A)=\frac{3}{5}$ and $P(B)=\frac{2}{7}$ and events are independent?

Answer: $\frac{6}{35}$. For independent events, multiply: $\frac{3}{5} \times \frac{2}{7} = \frac{6}{35}$.

Flashcard 22: What is $P(A\cup B)$ if $P(A)=\frac{1}{4}$, $P(B)=\frac{1}{3}$, and events are mutually exclusive?

Answer: $\frac{7}{12}$. For mutually exclusive events, add probabilities: $\frac{1}{4} + \frac{1}{3} = \frac{3}{12} + \frac{4}{12} = \frac{7}{12}$.

Flashcard 23: What is the probability of getting exactly one head in two fair coin flips?

Answer: $\frac{1}{2}$. Two coin flips yield four equally likely outcomes, with exactly one head in two of them (HT, TH).

Flashcard 24: What is the probability of drawing a red card from a standard $52$-card deck?

Answer: $\frac{1}{2}$. A standard deck has 52 cards, with 26 red cards equally likely to be drawn.

Flashcard 25: What is the probability formula when all outcomes are equally likely?

Answer: $P(\text{event})=\frac{\text{favorable outcomes}}{\text{total outcomes}}$. This formula divides the number of favorable outcomes by the total number of equally likely outcomes in the sample space.