AP Statistics Flashcards: Introduction To Probability

What this deck covers

This deck focuses on Introduction To Probability, giving you a quick way to review the definitions, rules, and examples that matter most for AP Statistics.

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: Identify the correct representation for the intersection of events $A$ and $B$.

Answer: $A \text{ and } B$. Intersection notation for events occurring together.

Flashcard 2: Identify the probability of a certain event.

Answer: The probability of a certain event is 1. An event that must occur has probability 1.

Flashcard 3: Identify the probability of rolling a number greater than 4 on a six-sided die.

Answer: $\frac{1}{3}$. Numbers 5 and 6 out of six possibilities.

Flashcard 4: What is meant by the sample space in probability?

Answer: The sample space is the set of all possible outcomes. Contains every possible outcome of an experiment.

Flashcard 5: What is the probability of an event that is certain to happen?

Answer: The probability is 1. Certain events have maximum probability.

Flashcard 6: Identify the term for $P(A|B)$.

Answer: Conditional probability. Represents probability of A given that B occurred.

Flashcard 7: Identify the probability of a single coin landing heads up.

Answer: $\frac{1}{2}$. Two equally likely outcomes: heads or tails.

Flashcard 8: What is the probability of drawing a red card from a standard deck?

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

Flashcard 9: State the probability of rolling a 3 on a fair six-sided die.

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

Flashcard 10: Identify the correct representation for the intersection of events $A$ and $B$.

Answer: $A \text{ and } B$. Intersection notation for events occurring together.

Flashcard 11: What is meant by the sample space in probability?

Answer: The sample space is the set of all possible outcomes. Contains every possible outcome of an experiment.

Flashcard 12: What is the multiplication rule for dependent events?

Answer: $P(A \text{ and } B) = P(A) \times P(B|A)$. Multiplies probability of first by conditional probability.

Flashcard 13: What is the probability of either event $A$ or event $B$ if they are mutually exclusive?

Answer: $P(A \text{ or } B) = P(A) + P(B)$. Mutually exclusive means no overlap, so probabilities add.

Flashcard 14: Choose the correct expression for the complement rule.

Answer: $P(E') = 1 - P(E)$. Standard complement rule formula.

Flashcard 15: What does it mean if two events are independent?

Answer: The occurrence of one event does not affect the probability of the other. Knowledge of one event doesn't change the other's probability.

Flashcard 16: What does it mean if two events are independent?

Answer: The occurrence of one event does not affect the probability of the other. Knowledge of one event doesn't change the other's probability.

Flashcard 17: Define what a 'simple event' is in probability.

Answer: A simple event consists of a single outcome. Contains exactly one outcome from the sample space.

Flashcard 18: State the formula for conditional probability.

Answer: $P(A|B) = \frac{P(A \text{ and } B)}{P(B)}$. Divides joint probability by the given event's probability.

Flashcard 19: Identify the probability of a single coin landing heads up.

Answer: $\frac{1}{2}$. Two equally likely outcomes: heads or tails.

Flashcard 20: What is 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 21: What is the probability of either event $A$ or event $B$ if they are mutually exclusive?

Answer: $P(A \text{ or } B) = P(A) + P(B)$. Mutually exclusive means no overlap, so probabilities add.

Flashcard 22: What is the probability of drawing a heart from a standard deck of cards?

Answer: $\frac{1}{4}$ or 0.25. 13 hearts out of 52 total cards.

Flashcard 23: Identify the term for $P(A|B)$.

Answer: Conditional probability. Represents probability of A given that B occurred.

Flashcard 24: Define the term 'event' in probability.

Answer: An event is a set of outcomes from a probability experiment. A collection of one or more outcomes.

Flashcard 25: State the formula for the probability of $A$ or $B$ when $A$ and $B$ are not mutually exclusive.

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

Flashcard 26: Define conditional probability.

Answer: Conditional probability is the probability of an event given another event. Probability of one event assuming another has occurred.

Flashcard 27: Choose the correct expression for the complement rule.

Answer: $P(E') = 1 - P(E)$. Standard complement rule formula.

Flashcard 28: If $P(A) = 0.3$ and $P(B) = 0.6$, find $P(A \text{ or } B)$ if $A$ and $B$ are mutually exclusive.

Answer: $P(A \text{ or } B) = 0.9$. Add probabilities since events cannot overlap.

Flashcard 29: What is the definition of probability?

Answer: Probability is the measure of the likelihood of an event occurring. Quantifies the likelihood on a scale from 0 to 1.

Flashcard 30: Define the term 'event' in probability.

Answer: An event is a set of outcomes from a probability experiment. A collection of one or more outcomes.

Flashcard 31: Identify the probability of an impossible event.

Answer: The probability of an impossible event is 0. An event that cannot occur has zero probability.

Flashcard 32: Find the probability of rolling an even number on a six-sided die.

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

Flashcard 33: Find the probability of rolling an even number on a six-sided die.

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

Flashcard 34: Define what a probability distribution is.

Answer: A probability distribution lists all the possible outcomes and their probabilities. Maps each outcome to its probability value.

Flashcard 35: What is the probability of the complement of an event?

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

Flashcard 36: Calculate $P(A \text{ and } B)$ given $P(A) = 0.4$, $P(B) = 0.5$, and $A$ and $B$ are independent.

Answer: $P(A \text{ and } B) = 0.2$. Multiply probabilities: $0.4 \times 0.5 = 0.2$.

Flashcard 37: Calculate $P(A \text{ and } B)$ given $P(A) = 0.4$, $P(B) = 0.5$, and $A$ and $B$ are independent.

Answer: $P(A \text{ and } B) = 0.2$. Multiply probabilities: $0.4 \times 0.5 = 0.2$.

Flashcard 38: State the probability of rolling a 3 on a fair six-sided die.

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

Flashcard 39: What is the probability of drawing a red card from a standard deck?

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

Flashcard 40: What is the probability of drawing an ace from a standard deck of cards?

Answer: $\frac{1}{13}$. Four aces in a standard 52-card deck.

Flashcard 41: Calculate $P(A')$ if $P(A) = 0.7$.

Answer: $P(A') = 0.3$. Using complement rule: $1 - 0.7 = 0.3$.

Flashcard 42: State the formula for the probability of $A$ or $B$ when $A$ and $B$ are not mutually exclusive.

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

Flashcard 43: What is the probability of drawing an ace from a standard deck of cards?

Answer: $\frac{1}{13}$. Four aces in a standard 52-card deck.

Flashcard 44: What is 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 45: Calculate $P(A')$ if $P(A) = 0.7$.

Answer: $P(A') = 0.3$. Using complement rule: $1 - 0.7 = 0.3$.

Flashcard 46: What is the probability of the complement of an event?

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

Flashcard 47: State the general addition rule for any two events.

Answer: $P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$. Subtracts overlap to avoid double-counting.

Flashcard 48: What is the multiplication rule for dependent events?

Answer: $P(A \text{ and } B) = P(A) \times P(B|A)$. Multiplies probability of first by conditional probability.

Flashcard 49: Define mutually exclusive events.

Answer: Mutually exclusive events cannot occur at the same time. Events with no shared outcomes.

Flashcard 50: Define what a 'simple event' is in probability.

Answer: A simple event consists of a single outcome. Contains exactly one outcome from the sample space.

Flashcard 51: Determine if events $A$ and $B$ are independent given $P(A|B) = P(A)$.

Answer: Events $A$ and $B$ are independent. When conditional equals marginal probability, events are independent.

Flashcard 52: Identify the probability of a certain event.

Answer: The probability of a certain event is 1. An event that must occur has probability 1.

Flashcard 53: What is the range of values for probability?

Answer: Probability values range from 0 to 1. 0 means impossible, 1 means certain.

Flashcard 54: Choose the term for $P(A \text{ and } B)$ when $A$ and $B$ are independent.

Answer: Joint probability. Describes the probability of both events occurring together.

Flashcard 55: If $P(A) = 0.3$ and $P(B) = 0.6$, find $P(A \text{ or } B)$ if $A$ and $B$ are mutually exclusive.

Answer: $P(A \text{ or } B) = 0.9$. Add probabilities since events cannot overlap.

Flashcard 56: Choose the correct term for $P(E')$.

Answer: Complement of event $E$. Standard notation for the complement of event E.

Flashcard 57: What is the range of values for probability?

Answer: Probability values range from 0 to 1. 0 means impossible, 1 means certain.

Flashcard 58: State the addition rule for mutually exclusive events.

Answer: $P(A \text{ or } B) = P(A) + P(B)$. For mutually exclusive events, probabilities simply add.

Flashcard 59: Define what a probability distribution is.

Answer: A probability distribution lists all the possible outcomes and their probabilities. Maps each outcome to its probability value.

Flashcard 60: State the formula for the probability of an event.

Answer: $P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. Classic formula dividing favorable by total outcomes.

Flashcard 61: State the formula for the probability of an event.

Answer: $P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$

Flashcard 62: State the formula for conditional probability.

Answer: $P(A|B) = \frac{P(A \text{ and } B)}{P(B)}$. Divides joint probability by the given event's probability.

Flashcard 63: Define mutually exclusive events.

Answer: Mutually exclusive events cannot occur at the same time. Events with no shared outcomes.

Flashcard 64: Determine if events $A$ and $B$ are independent given $P(A|B) = P(A)$.

Answer: Events $A$ and $B$ are independent. When conditional equals marginal probability, events are independent.

Flashcard 65: Identify the probability of rolling a number greater than 4 on a six-sided die.

Answer: $\frac{1}{3}$. Numbers 5 and 6 out of six possibilities.

Flashcard 66: What is the probability of an event that is certain to happen?

Answer: The probability is 1. Certain events have maximum probability.

Flashcard 67: State the addition rule for mutually exclusive events.

Answer: $P(A \text{ or } B) = P(A) + P(B)$. For mutually exclusive events, probabilities simply add.

Flashcard 68: Choose the correct term for $P(E')$.

Answer: Complement of event $E$. Standard notation for the complement of event E.

Flashcard 69: Identify the probability of an impossible event.

Answer: The probability of an impossible event is 0. An event that cannot occur has zero probability.

Flashcard 70: What does $P(\text{not } A)$ represent?

Answer: The probability that event $A$ does not occur. Standard notation for complement probability.

Flashcard 71: Choose the term for $P(A \text{ and } B)$ when $A$ and $B$ are independent.

Answer: Joint probability. Describes the probability of both events occurring together.

Flashcard 72: What is the definition of probability?

Answer: Probability is the measure of the likelihood of an event occurring. Quantifies the likelihood on a scale from 0 to 1.

Flashcard 73: What does the term 'outcome' refer to in probability?

Answer: An outcome is a possible result of a probability experiment. A single possible result from an experiment.

Flashcard 74: State the general addition rule for any two events.

Answer: $P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$. Subtracts overlap to avoid double-counting.

Flashcard 75: Define conditional probability.

Answer: Conditional probability is the probability of an event given another event. Probability of one event assuming another has occurred.

Flashcard 76: What does $P(\text{not } A)$ represent?

Answer: The probability that event $A$ does not occur. Standard notation for complement probability.

Flashcard 77: What does the term 'outcome' refer to in probability?

Answer: An outcome is a possible result of a probability experiment. A single possible result from an experiment.

Flashcard 78: What is the probability of drawing a heart from a standard deck of cards?

Answer: $\frac{1}{4}$ or 0.25. 13 hearts out of 52 total cards.