ISEE Middle Level Quantitative Reasoning Flashcards: Basic Probability

What this deck covers

This deck focuses on Basic Probability, giving you a quick way to review the definitions, rules, and examples that matter most for ISEE Middle Level Quantitative Reasoning.

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: A bag has $3$ red and $2$ blue marbles. What is $P(\text{red})$ on one draw?

Answer: $\frac{3}{5}$. There are 3 red marbles out of 5 total marbles in the bag.

Flashcard 2: A bag has $3$ red and $2$ blue marbles. Without replacement, what is $P(\text{red then red})$?

Answer: $\frac{3}{10}$. Without replacement, multiply $\frac{3}{5}$ by $\frac{2}{4}$ for two red draws.

Flashcard 3: A bag has $3$ red and $2$ blue marbles. With replacement, what is $P(\text{red then red})$?

Answer: $\frac{9}{25}$. With replacement, the probability remains $\frac{3}{5}$ for each independent draw, so multiply.

Flashcard 4: What is the probability of getting heads on a fair coin flip?

Answer: $\frac{1}{2}$. One favorable outcome (heads) out of two equally likely outcomes on a fair coin.

Flashcard 5: What is the probability of an event $E$ if it has $f$ favorable outcomes out of $n$ equally likely outcomes?

Answer: $P(E)=\frac{f}{n}$. Probability is defined as the ratio of the number of favorable outcomes to the total number of equally likely outcomes.

Flashcard 6: What is the probability of an event that is impossible (has $0$ favorable outcomes)?

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

Flashcard 7: What is the probability of an event that is certain (always occurs)?

Answer: $1$. A certain event includes all possible outcomes, so its probability equals one.

Flashcard 8: What is the relationship between an event $E$ and its complement $E^c$?

Answer: $P(E^c)=1-P(E)$. The probability of the complement is one minus the event's probability, as they together cover all outcomes.

Flashcard 9: What is $P(E)$ if $P(E^c)=\frac{3}{8}$?

Answer: $\frac{5}{8}$. Subtract the probability of the complement from 1 to find the event's probability.

Flashcard 10: What is $P(E^c)$ if $P(E)=0.27$?

Answer: $0.73$. The complement's probability is 1 minus the event's probability.

Flashcard 11: What is the probability of rolling a $4$ on a fair six-sided die?

Answer: $\frac{1}{6}$. One favorable outcome (rolling a 4) out of six equally likely outcomes on a fair die.

Flashcard 12: What is the probability of rolling an even number on a fair six-sided die?

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

Flashcard 13: What is the probability of getting at least one head in two fair coin flips?

Answer: $\frac{3}{4}$. Calculated as 1 minus the probability of no heads (both tails), which is $\frac{1}{4}$.

Flashcard 14: What is the probability of getting two heads in two fair coin flips?

Answer: $\frac{1}{4}$. The probability of heads on each independent flip is $\frac{1}{2}$, so multiply for both.

Flashcard 15: 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 in a standard deck.

Flashcard 16: What is the probability of drawing an ace from a standard $52$-card deck?

Answer: $\frac{1}{13}$. There are 4 aces out of 52 cards in a standard deck.

Flashcard 17: 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 in a standard deck.

Flashcard 18: What is the probability of drawing a face card (J, Q, or K) from a $52$-card deck?

Answer: $\frac{3}{13}$. There are 12 face cards (3 per suit, 4 suits) out of 52 in a standard deck.

Flashcard 19: 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's probability is the sum since there is no overlap.

Flashcard 20: If events $A$ and $B$ are mutually exclusive, what is $P(A\cap B)$?

Answer: $0$. Mutually exclusive events cannot occur together, so their intersection has zero probability.

Flashcard 21: If $P(A)=\frac{1}{5}$ and $P(B)=\frac{2}{5}$ and $A,B$ are mutually exclusive, what is $P(A\cup B)$?

Answer: $\frac{3}{5}$. Add the probabilities since the events are mutually exclusive with no overlap.

Flashcard 22: What is the general addition rule for any events $A$ and $B$ (not necessarily disjoint)?

Answer: $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. The general rule accounts for overlap by subtracting the intersection's probability.

Flashcard 23: If $P(A)=0.6$, $P(B)=0.5$, and $P(A\cap B)=0.2$, what is $P(A\cup B)$?

Answer: $0.9$. Apply the general addition rule: add probabilities and subtract the intersection.

Flashcard 24: What is the multiplication rule for independent events $A$ and $B$?

Answer: $P(A\cap B)=P(A)P(B)$. For independent events, the joint probability is the product of individual probabilities.

Flashcard 25: If $P(A)=\frac{3}{10}$ and $P(B)=\frac{1}{2}$ and $A,B$ are independent, what is $P(A\cap B)$?

Answer: $\frac{3}{20}$. Multiply the probabilities since the events are independent.