Probability - SAT Math

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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.

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

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

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

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

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

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

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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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