ISEE Upper Level Mathematics Achievement Flashcards: Single And Compound Probability

What this deck covers

This deck focuses on Single And Compound Probability, giving you a quick way to review the definitions, rules, and examples that matter most for ISEE Upper 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 rolling a $2$ or a $5$ on one fair die?

Answer: $\frac{1}{3}$. Two favorable outcomes ($2$ or $5$) out of six, and events are mutually exclusive.

Flashcard 2: What is the general addition rule for any events $A$ and $B$?

Answer: $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. Accounts for overlap by subtracting the intersection probability from the sum of individual probabilities.

Flashcard 3: What is the probability of drawing a red card from a standard $52$-card deck?

Answer: $\frac{1}{2}$. There are $26$ red cards (hearts and diamonds) out of $52$ total cards.

Flashcard 4: What is the complement rule for an event $A$ in probability notation?

Answer: $P(A^c)=1-P(A)$. Calculates the probability of the complement by subtracting the event's probability from 1, as they are mutually exclusive and exhaustive.

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

Answer: $\frac{1}{13}$. Four aces (one per suit) out of $52$ cards in the deck.

Flashcard 6: What is $P(A\cap B)$ if $P(A)=\frac{2}{5}$ and $P(B\mid A)=\frac{3}{4}$?

Answer: $\frac{3}{10}$. Multiplies $P(A)$ by conditional $P(B\mid A)$ for joint probability of dependent events.

Flashcard 7: What is the probability of rolling a $6$ on a fair six-sided die?

Answer: $\frac{1}{6}$. One favorable outcome ($6$) out of six equally likely faces on the die.

Flashcard 8: What is the probability of drawing two aces in a row without replacement from a $52$-card deck?

Answer: $\frac{4}{52}\cdot\frac{3}{51}=\frac{1}{221}$. Multiplies probabilities of drawing first ace then second without replacement.

Flashcard 9: What is the probability of rolling doubles with two fair six-sided dice?

Answer: $\frac{1}{6}$. Six double outcomes out of $36$ total combinations for two dice.

Flashcard 10: What is the addition rule for mutually exclusive events $A$ and $B$?

Answer: $P(A\cup B)=P(A)+P(B)$. Adds probabilities directly for mutually exclusive events since their intersection is empty.

Flashcard 11: What is the probability formula for an event $A$ using favorable and total outcomes?

Answer: $P(A)=\frac{\text{favorable}}{\text{total}}$. Defines probability as the ratio of favorable outcomes to total possible outcomes in a sample space.

Flashcard 12: What is the probability of drawing a face card (J, Q, or K) from a $52$-card deck?

Answer: $\frac{3}{13}$. Twelve face cards ($3$ per suit across $4$ suits) out of $52$ total cards.

Flashcard 13: What is $P(\text{not }6)$ when rolling one fair die?

Answer: $\frac{5}{6}$. Uses the complement rule: $1$ minus the probability of rolling a $6$ ($\frac{1}{6}$).

Flashcard 14: What is the probability of flipping two fair coins and getting exactly one head?

Answer: $\frac{1}{2}$. Two favorable outcomes (HT, TH) out of four possible results for two coins.

Flashcard 15: What is the probability of drawing two red cards in a row with replacement from a $52$-card deck?

Answer: $\frac{1}{2}\cdot\frac{1}{2}=\frac{1}{4}$. Independent draws with replacement, each with $\frac{1}{2}$ probability of red.

Flashcard 16: What is the probability of rolling two fair dice and getting a sum of $7$?

Answer: $\frac{1}{6}$. Six ways to get sum $7$ out of $36$ possible outcomes for two dice.

Flashcard 17: What is the probability of flipping two fair coins and getting two heads?

Answer: $\frac{1}{4}$. Independent coin flips each with $\frac{1}{2}$ probability of heads, multiplied for both.

Flashcard 18: What is the conditional probability formula for $P(A\mid B)$?

Answer: $P(A\mid B)=\frac{P(A\cap B)}{P(B)}$. Divides the joint probability by the probability of the conditioning event to find the likelihood given that event.

Flashcard 19: What is the probability of rolling an even number on a fair die?

Answer: $\frac{1}{2}$. Three even numbers ($2,4,6$) out of six possible outcomes on the die.

Flashcard 20: What is the probability of flipping a fair coin and getting heads?

Answer: $\frac{1}{2}$. Two equally likely outcomes (heads or tails) on a fair coin, with one favorable.

Flashcard 21: What is the multiplication rule for dependent events using conditional probability?

Answer: $P(A\cap B)=P(A)P(B\mid A)$. Expresses joint probability using the initial event and the conditional probability for dependent events.

Flashcard 22: What is the probability of drawing a heart from a standard $52$-card deck?

Answer: $\frac{1}{4}$. There are $13$ hearts out of $52$ cards, yielding the ratio of favorable to total outcomes.

Flashcard 23: What is the multiplication rule for independent events $A$ and $B$?

Answer: $P(A\cap B)=P(A)P(B)$. Multiplies probabilities for independent events because one does not affect the other.

Flashcard 24: What is $P(A\cup B)$ if $P(A)=\frac{1}{3}$, $P(B)=\frac{1}{4}$, and $A,B$ are mutually exclusive?

Answer: $\frac{7}{12}$. Adds probabilities since events are mutually exclusive, with no overlap.

Flashcard 25: What is the probability of drawing two hearts in a row without replacement from a $52$-card deck?

Answer: $\frac{13}{52}\cdot\frac{12}{51}=\frac{1}{17}$. Multiplies conditional probabilities for first and second heart without replacement.