SAT Math Flashcards: Probability

What this deck covers

This deck focuses on Probability, giving you a quick way to review the definitions, rules, and examples that matter most for SAT Math.

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 sum of 7 with two dice?

Answer: $\frac{1}{6}$. 6 ways to roll 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1).

Flashcard 2: What is the probability of rolling a 3 on a fair 6-sided die?

Answer: Probability = $\frac{1}{6}$. One favorable outcome (rolling 3) out of six possible outcomes.

Flashcard 3: What is the probability of drawing a diamond from a deck of 52 cards?

Answer: $\frac{1}{4}$. 13 diamonds out of 52 total cards.

Flashcard 4: If $P(A) = 0.3$ and $P(B) = 0.4$, find $P(A \text{ or } B)$ assuming independence.

Answer: $0.58$. Using addition rule: $0.3 + 0.4 - (0.3 \times 0.4) = 0.58$.

Flashcard 5: State the formula for the probability of the complement of an event.

Answer: P(A') = 1 - P(A). Complement probability equals 1 minus the original event's probability.

Flashcard 6: Define mutually exclusive events.

Answer: Events that cannot occur simultaneously. If one occurs, the other cannot happen at the same time.

Flashcard 7: What is the probability of rolling a prime number on a 6-sided die?

Answer: $\frac{1}{2}$. Prime numbers on die: 2, 3, 5 (three out of six).

Flashcard 8: If $P(A) = 0.5$, what is $P(A')$?

Answer: $0.5$. Complement of A: $1 - 0.5 = 0.5$.

Flashcard 9: What is the probability of at least one head in two coin flips?

Answer: $\frac{3}{4}$. Complement of all tails: $1 - \frac{1}{4} = \frac{3}{4}$.

Flashcard 10: What is the probability of drawing an ace or a king from a deck?

Answer: $\frac{2}{13}$. 8 favorable cards (4 aces + 4 kings) out of 52 total.

Flashcard 11: What is the probability of rolling a 3 on a fair 6-sided die?

Answer: Probability = $\frac{1}{6}$. One favorable outcome (rolling 3) out of six possible outcomes.

Flashcard 12: What is the sum of probabilities for all possible outcomes of an event?

Answer:

1. All possible outcomes together form the complete sample space.

Flashcard 13: What is the probability of rolling a prime number on a 6-sided die?

Answer: $\frac{1}{2}$. Prime numbers on die: 2, 3, 5 (three out of six).

Flashcard 14: What is the probability of flipping a coin and getting heads?

Answer: Probability = $\frac{1}{2}$. One favorable outcome (heads) out of two possible outcomes.

Flashcard 15: What is $P(A \text{ and } B)$ if $P(A) = 0.3$ and $P(B) = 0.2$ assuming independence?

Answer: $0.06$. Multiply independent probabilities: $0.3 \times 0.2 = 0.06$.

Flashcard 16: State the formula for the probability of the complement of an event.

Answer: $P(A') = 1 - P(A)$. Complement probability equals 1 minus the original event's probability.

Flashcard 17: What is the probability of drawing a heart from a standard deck of 52 cards?

Answer: $\frac{1}{4}$. 13 hearts out of 52 total cards simplifies to $\frac{1}{4}$.

Flashcard 18: What is $P(A \text{ and } B)$ for independent events A and B?

Answer: $P(A \text{ and } B) = P(A) \times P(B)$. For independent events, multiply their individual probabilities.

Flashcard 19: Identify the probability of rolling an even number on a fair 6-sided die.

Answer: Probability = $\frac{3}{6}$ or $\frac{1}{2}$. Three even numbers (2, 4, 6) out of six possible outcomes.

Flashcard 20: What is the probability of flipping two heads on two fair coins?

Answer: $\frac{1}{4}$. Multiply independent probabilities: $\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$.

Flashcard 21: State the formula for conditional probability $P(A|B)$.

Answer: $P(A|B) = \frac{P(A \text{ and } B)}{P(B)}$. Probability of A given B has occurred.

Flashcard 22: Define independent events.

Answer: Events where the occurrence of one does not affect the other. One event's outcome doesn't change the other's probability.

Flashcard 23: What is the probability of drawing a red ace from a deck of cards?

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

Flashcard 24: State the formula for the probability of the complement of event A.

Answer: $P(A') = 1 - P(A)$. The complement probability equals 1 minus the event probability.

Flashcard 25: What is the probability of drawing a black card from a standard deck?

Answer: $\frac{1}{2}$. 26 black cards (spades and clubs) out of 52 total.

Flashcard 26: Define mutually exclusive events.

Answer: Events that cannot occur simultaneously. If one occurs, the other cannot happen at the same time.

Flashcard 27: What is the probability of rolling a 4 on a fair 6-sided die?

Answer: $\frac{1}{6}$. One favorable outcome out of six possible outcomes.

Flashcard 28: What is the probability of flipping two heads on two fair coins?

Answer: $\frac{1}{4}$. Multiply independent probabilities: $\frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$.

Flashcard 29: Define exhaustive events.

Answer: A set of events that cover all possible outcomes. Events whose probabilities sum to 1 (complete sample space).

Flashcard 30: What is the probability of at least one head in two coin flips?

Answer: $\frac{3}{4}$. Complement of all tails: $1 - \frac{1}{4} = \frac{3}{4}$.

Flashcard 31: What is the probability of drawing an ace or a king from a deck?

Answer: $\frac{2}{13}$. 8 favorable cards (4 aces + 4 kings) out of 52 total.

Flashcard 32: Define exhaustive events.

Answer: A set of events that cover all possible outcomes. Events whose probabilities sum to 1 (complete sample space).

Flashcard 33: What is the probability of drawing a red queen or a black king from a deck?

Answer: $\frac{1}{13}$. 2 red queens + 2 black kings = 4 favorable cards out of 52.

Flashcard 34: What is the sum of probabilities for all possible outcomes of an event?

Answer:

1. All possible outcomes together form the complete sample space.

Flashcard 35: What is the probability of drawing a red ace from a deck of cards?

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

Flashcard 36: What is the probability of rolling a total of 4 with two dice?

Answer: $\frac{1}{12}$. 3 ways to roll 4: (1,3), (2,2), (3,1) out of 36 possibilities.

Flashcard 37: If two events A and B are mutually exclusive, what is $P(A \text{ and } B)$?

Answer: $P(A \text{ and } B) = 0$. Mutually exclusive events cannot happen together.

Flashcard 38: State the formula for the probability of independent events A and B both occurring.

Answer: $P(A \text{ and } B) = P(A) \times P(B)$. For independent events, multiply individual probabilities.

Flashcard 39: What is the probability of rolling an even number on a 6-sided die?

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

Flashcard 40: Define complementary events.

Answer: Two events are complementary if one event is the complement of the other. One event is exactly the opposite of the other.

Flashcard 41: What is $P(A \text{ or } B)$ if $P(A) = 0.3$, $P(B) = 0.4$, and $P(A \text{ and } B) = 0.2$?

Answer: $0.5$. Apply addition rule: $0.3 + 0.4 - 0.2 = 0.5$.

Flashcard 42: What is the probability of not drawing a face card from a deck of cards?

Answer: $\frac{10}{13}$. 40 non-face cards out of 52 total cards.

Flashcard 43: What is the probability formula for a single event occurring?

Answer: Probability = (Number of favorable outcomes) / (Total number of possible outcomes). This is the fundamental definition of probability in statistics.

Flashcard 44: Identify the probability of drawing a heart from a standard deck of cards.

Answer: 1/4. 13 hearts out of 52 total cards in a standard deck.

Flashcard 45: What is the probability of drawing a diamond from a deck of 52 cards?

Answer: $\frac{1}{4}$. 13 diamonds out of 52 total cards.

Flashcard 46: What is the probability of drawing a queen from a shuffled deck of 52 cards?

Answer: $\frac{1}{13}$. 4 queens out of 52 cards simplifies to $\frac{1}{13}$.

Flashcard 47: What is the probability of not drawing a face card from a deck of cards?

Answer: $\frac{10}{13}$. 40 non-face cards out of 52 total cards.

Flashcard 48: What is the probability of rolling a 4 on a fair 6-sided die?

Answer: $\frac{1}{6}$. One favorable outcome out of six possible outcomes.

Flashcard 49: What is the probability of flipping a coin and getting heads?

Answer: Probability = $\frac{1}{2}$. One favorable outcome (heads) out of two possible outcomes.

Flashcard 50: What is the probability of getting at least one 6 when rolling two dice?

Answer: $\frac{11}{36}$. Use complement: $1 - P(\text{no 6s}) = 1 - \frac{25}{36} = \frac{11}{36}$.

Flashcard 51: What is the probability of drawing a red card after drawing a black card without replacement?

Answer: $\frac{26}{51}$. After removing one black card, 26 red remain out of 51 total.

Flashcard 52: What is the probability of not rolling a 3 on a fair 6-sided die?

Answer: $\frac{5}{6}$. Complement of rolling a 3: $1 - \frac{1}{6} = \frac{5}{6}$.

Flashcard 53: Define independent events.

Answer: Events where the occurrence of one does not affect the other. One event's outcome doesn't change the other's probability.

Flashcard 54: Identify the probability of drawing an ace from a standard deck of 52 cards.

Answer: Probability = $\frac{4}{52}$ or $\frac{1}{13}$. Four aces in a standard deck of 52 cards.

Flashcard 55: What is the probability of drawing a card that is either a club or a face card?

Answer: $\frac{5}{13}$. 13 clubs + 12 face cards - 3 club face cards = 22 favorable.

Flashcard 56: Identify the probability of drawing a heart from a standard deck of 52 cards.

Answer: Probability = $\frac{13}{52}$ or $\frac{1}{4}$. Thirteen hearts in a standard deck of 52 cards.

Flashcard 57: Identify the probability of drawing a heart from a standard deck of 52 cards.

Answer: Probability = $\frac{13}{52}$ or $\frac{1}{4}$. Thirteen hearts in a standard deck of 52 cards.

Flashcard 58: What is the probability of getting a sum of 7 when rolling two fair 6-sided dice?

Answer: Probability = $\frac{6}{36}$ or $\frac{1}{6}$. Six ways to make 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) out of 36 total.

Flashcard 59: State the multiplication rule for independent events.

Answer: $P(A \text{ and } B) = P(A) \times P(B)$. For independent events, probability of both occurring.

Flashcard 60: State the addition rule for probability.

Answer: $P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$. General formula accounting for overlap between events.

Flashcard 61: What is the probability of drawing a red card after drawing a black card without replacement?

Answer: $\frac{26}{51}$. After removing one black card, 26 red remain out of 51 total.

Flashcard 62: What is the probability of drawing a red card from a standard deck of 52 cards?

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

Flashcard 63: State the addition rule for probability.

Answer: $P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$. General formula accounting for overlap between events.

Flashcard 64: What is $P(A \text{ or } B)$ if $P(A) = 0.3$, $P(B) = 0.4$, and $P(A \text{ and } B) = 0.2$?

Answer: $0.5$. Apply addition rule: $0.3 + 0.4 - 0.2 = 0.5$.

Flashcard 65: What is the probability of getting a sum of 7 when rolling two fair 6-sided dice?

Answer: Probability = $\frac{6}{36}$ or $\frac{1}{6}$. Six ways to make 7: (1,6), (2,5), (3,4), (4,3), (5,2), (6,1) out of 36 total.

Flashcard 66: State the addition rule for probability of mutually exclusive events.

Answer: P(A or B) = P(A) + P(B). For mutually exclusive events, probabilities add since they cannot occur together.

Flashcard 67: State the formula for calculating probability.

Answer: $P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. Basic probability definition using favorable over total outcomes.

Flashcard 68: What is the probability of getting at least one 6 when rolling two dice?

Answer: $\frac{11}{36}$. Use complement: $1 - P(\text{no 6s}) = 1 - \frac{25}{36} = \frac{11}{36}$.

Flashcard 69: What is the probability of not rolling a 3 on a fair 6-sided die?

Answer: $\frac{5}{6}$. Complement of rolling a 3: $1 - \frac{1}{6} = \frac{5}{6}$.

Flashcard 70: What is the probability of drawing a queen from a shuffled deck of 52 cards?

Answer: $\frac{1}{13}$. 4 queens out of 52 cards simplifies to $\frac{1}{13}$.

Flashcard 71: State the formula for calculating probability.

Answer: Probability = $\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. Basic probability definition: favorable outcomes divided by total outcomes.

Flashcard 72: What is the probability of getting two tails in three coin flips?

Answer: $\frac{3}{8}$. Count outcomes with exactly two tails: TTH, THT, HTT.

Flashcard 73: If $P(A) = 0.5$, what is $P(A')$?

Answer: $0.5$. Complement of A: $1 - 0.5 = 0.5$.

Flashcard 74: What is the probability of drawing two aces in a row from a deck without replacement?

Answer: $\frac{1}{221}$. First ace: $\frac{4}{52}$, second ace: $\frac{3}{51}$, multiply together.

Flashcard 75: Identify the probability of rolling an even number on a fair 6-sided die.

Answer: Probability = $\frac{3}{6}$ or $\frac{1}{2}$. Three even numbers (2, 4, 6) out of six possible outcomes.

Flashcard 76: State the formula for calculating probability.

Answer: $P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. Basic probability definition using favorable over total outcomes.

Flashcard 77: What is the probability of drawing a card that is either a club or a face card?

Answer: $\frac{5}{13}$. 13 clubs + 12 face cards - 3 club face cards = 22 favorable.

Flashcard 78: What is the probability of drawing a black card from a standard deck?

Answer: $\frac{1}{2}$. 26 black cards (spades and clubs) out of 52 total.

Flashcard 79: What is the probability formula for a single event occurring?

Answer: Probability = (Number of favorable outcomes) / (Total number of possible outcomes). This is the fundamental definition of probability in statistics.

Flashcard 80: State the multiplication rule for independent events.

Answer: $P(A \text{ and } B) = P(A) \times P(B)$. For independent events, probability of both occurring.

Flashcard 81: State the formula for conditional probability $P(A|B)$.

Answer: $P(A|B) = \frac{P(A \text{ and } B)}{P(B)}$. Probability of A given B has occurred.

Flashcard 82: Define complementary events.

Answer: Two events are complementary if one event is the complement of the other. One event is exactly the opposite of the other.

Flashcard 83: What is the probability of drawing a spade or a face card from a deck?

Answer: $\frac{11}{26}$. 13 spades + 12 face cards - 3 overlap = 22 favorable outcomes.

Flashcard 84: Identify the probability of rolling a 4 on a standard 6-sided die.

Answer: 1/6. One specific outcome (rolling 4) out of six equally likely outcomes.

Flashcard 85: What is the probability of drawing a red card from a standard deck of 52 cards?

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

Flashcard 86: What is the probability of drawing a king or a heart from a deck of cards?

Answer: $\frac{4}{13}$. 4 kings + 13 hearts - 1 king of hearts = 16 favorable.

Flashcard 87: What is the probability of drawing a red queen or a black king from a deck?

Answer: $\frac{1}{13}$. 2 red queens + 2 black kings = 4 favorable cards out of 52.

Flashcard 88: What is the probability of drawing a spade or a face card from a deck?

Answer: $\frac{11}{26}$. 13 spades + 12 face cards - 3 overlap = 22 favorable outcomes.

Flashcard 89: What is the probability of rolling a total of 4 with two dice?

Answer: $\frac{1}{12}$. 3 ways to roll 4: (1,3), (2,2), (3,1) out of 36 possibilities.

Flashcard 90: What is the probability of getting two tails in three coin flips?

Answer: $\frac{3}{8}$. Count outcomes with exactly two tails: TTH, THT, HTT.

Flashcard 91: What is $P(A \text{ and } B)$ for independent events A and B?

Answer: $P(A \text{ and } B) = P(A) \times P(B)$. For independent events, multiply their individual probabilities.

Flashcard 92: What is the probability of drawing two aces in a row from a deck without replacement?

Answer: $\frac{1}{221}$. First ace: $\frac{4}{52}$, second ace: $\frac{3}{51}$, multiply together.

Flashcard 93: Identify the probability of drawing an ace from a standard deck of 52 cards.

Answer: Probability = $\frac{4}{52}$ or $\frac{1}{13}$. Four aces in a standard deck of 52 cards.

Flashcard 94: If two events A and B are mutually exclusive, what is $P(A \text{ and } B)$?

Answer: $P(A \text{ and } B) = 0$. Mutually exclusive events cannot happen together.

Flashcard 95: What is $P(A \text{ and } B)$ if $P(A) = 0.3$ and $P(B) = 0.2$ assuming independence?

Answer: $0.06$. Multiply independent probabilities: $0.3 \times 0.2 = 0.06$.

Flashcard 96: What is the probability of drawing a king or a heart from a deck of cards?

Answer: $\frac{4}{13}$. 4 kings + 13 hearts - 1 king of hearts = 16 favorable.

Flashcard 97: State the formula for the probability of the complement of event A.

Answer: $P(A') = 1 - P(A)$. The complement probability equals 1 minus the event probability.

Flashcard 98: What is the probability of drawing a heart from a standard deck of 52 cards?

Answer: $\frac{1}{4}$. 13 hearts out of 52 total cards simplifies to $\frac{1}{4}$.

Flashcard 99: What is the probability of rolling an even number on a 6-sided die?

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

Flashcard 100: Define dependent events.

Answer: Events where the occurrence of one affects the probability of the other. One event's outcome changes the probability of the other.