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Probability and Distributions Flashcards

7 cards from real AP practice questions. Tap to flip, then mark Knew It or Still Learning — missed cards come back until you master them.

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  1. Bayes' Theorem is used to:

    Answer: Update the probability of an event given new evidence

    Bayes' Theorem provides a way to revise prior probabilities when new information becomes available.

  2. A random variable X has E[X] = 5 and E[X²] = 30. What is Var(X)?

    Answer: 5

    Var(X) = E[X²] − (E[X])² = 30 − 25 = 5.

  3. If 2% of a population has a disease and a test is 90% sensitive and 95% specific, what concept describes the probability the disease is present given a positive test?

    Answer: Positive predictive value (Bayes' Theorem)

    Positive predictive value, computed via Bayes' Theorem, gives P(disease | positive test).

  4. For the standard normal distribution, P(−1.65 < Z < 1.65) is closest to:

    Answer: 0.90

    z = ±1.645 captures the middle 90% of the standard normal distribution.

  5. Two cards are drawn with replacement from a standard deck. What is P(both are aces)?

    Answer: 1/169

    With replacement, each draw is independent: (4/52) × (4/52) = 1/169.

  6. A linear transformation Y = 3X + 4 is applied to a random variable X with mean 6 and variance 4. What is E[Y]?

    Answer: 22

    E[Y] = 3·E[X] + 4 = 3(6) + 4 = 22.

  7. Which statement about the normal distribution is correct?

    Answer: It is completely described by its mean and standard deviation

    The normal distribution is fully characterized by μ (mean) and σ (standard deviation), and is symmetric.