Probability - SAT Math

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

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

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

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

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.

$\frac{1}{26}$. 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.

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

$0.06$. 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.

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

$\frac{1}{4}$. 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 $\frac{1}{4}$.

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

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.

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