AP Stats Probability

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What is conditional probability?

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Conditional probability is the probability of an event occurring given that another event has already occurred. It is denoted as P(A|B), which means the probability of A given B.

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What is the formula for calculating conditional probability?

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The formula for conditional probability is P(A|B) = P(A and B) / P(B), where P(A and B) is the probability of both events occurring.

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What does it mean if two events are independent?

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Two events are independent if the occurrence of one event does not affect the probability of the other event occurring. Mathematically, P(A and B) = P(A) * P(B).

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How do you calculate the expected value of a random variable?

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The expected value (E) of a random variable is calculated by summing the products of each possible value and its probability: E(X) = Σ [x * P(x)].

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What is the law of total probability?

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The law of total probability states that if B1, B2, ..., Bn are mutually exclusive events that cover the entire sample space, then P(A) = Σ P(A|Bi) * P(Bi).

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What is the difference between discrete and continuous random variables?

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Discrete random variables can take on a countable number of values, while continuous random variables can take on an infinite number of values within a given range.

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What is the probability of the complement of an event?

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The probability of the complement of an event A, denoted as A', is given by P(A') = 1 - P(A).

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How do you find the probability of the union of two events?

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The probability of the union of two events A and B is calculated using the formula: P(A or B) = P(A) + P(B) - P(A and B).

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What is a probability distribution?

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A probability distribution is a function that describes the likelihood of obtaining the possible values that a random variable can take.

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What is the significance of the normal distribution in statistics?

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The normal distribution is significant because many statistical methods assume that data follows a normal distribution, and it is characterized by its bell-shaped curve.