Practice quiz · by a Quizcard user

AP Statistics: Probability, Random Variables and Sampling Distributions — quiz

14 multiple-choice questions covering Addition Rule, Complement Rule, Conditional Probability, Independence vs. Mutually Exclusive, Expected Value. One answer each; you get a score at the end and the explanation for every question. No account needed.

Updated 2026-11-03. Keys 1–4 pick an answer, Enter moves on. Redo it any time, in order or shuffled.

The questions

Answers and explanations are shown after you finish.

1. Addition Rule

   In a class, 45% of students play a sport, 30% play an instrument, and 10% do both. What is the probability a randomly chosen student plays a sport or an instrument?

   • 0.85
   • 0.65
   • 0.75
   • 0.55
2. Complement Rule

   A player makes each free throw independently with probability 0.8. She shoots 3 free throws. What is the probability she makes at least one?

   • 0.488
   • 0.008
   • 0.8
   • 0.992
3. Conditional Probability

   Of 100 students, 40 play a sport and 25 of those 40 are also on the honor roll. What is P(honor roll | plays a sport)?

   • 0.25
   • 0.625
   • 0.40
   • 0.16
4. Independence vs. Mutually Exclusive

   Events A and B are mutually exclusive and both have positive probability. What must be true of A and B?

   • Equally likely
   • Complementary
   • Independent
   • Dependent
5. Expected Value

   A random variable X takes values 0, 1, 2 with probabilities 0.5, 0.3, and 0.2. What is E(X)?

   • 1.5
   • 0.5
   • 1.0
   • 0.7
6. Variance of a Random Variable

   X takes values 1 and 2 with probabilities 0.4 and 0.6 (so μ_X = 1.6). What is the variance of X?

   • 0.49
   • 0.16
   • 0.24
   • 0.36
7. Linear Transformations

   If Y = 5 + 2X, and X has mean 10 and standard deviation 3, what are the mean and standard deviation of Y?

   • μ=25, σ=6
   • μ=20, σ=3
   • μ=25, σ=11
   • μ=15, σ=6
8. Combining Random Variables

   X and Y are independent random variables with σ²_X = 4 and σ²_Y = 9. What is the variance of X − Y?

   • 13
   • 3.6
   • -5
   • 5
9. Binomial Setting (BINS)

   A researcher draws cards one at a time without replacement from a 10-card deck, recording whether each is a heart. Which BINS condition is violated?

   • Binary outcomes
   • Independent trials
   • Same probability of success
   • Fixed number of trials
10. Binomial Probability

    For a binomial situation with n = 6 and p = 0.4, what is P(X = 2)?

    • 0.311
    • 0.187
    • 0.254
    • 0.400
11. Binomial Mean & SD

    For a binomial random variable with n = 50 and p = 0.2, what are the mean and standard deviation?

    • μ=10, σ≈1.41
    • μ=10, σ≈2.83
    • μ=10, σ≈8.00
    • μ=40, σ≈2.83
12. Geometric Setting (BITS)

    An inspector tests light bulbs one at a time until the first defective bulb is found. Which distribution models the number of bulbs tested?

    • Normal
    • Uniform
    • Geometric
    • Binomial
13. Geometric Probability

    If p = 0.1, what is the probability that the first success occurs on the 5th trial?

    • 0.3439
    • 0.1000
    • 0.5000
    • 0.0656
14. Geometric Distribution Shape

    Compared to a binomial distribution, how does the shape of a geometric distribution typically behave?

    • Symmetric when p=0.5
    • Approximately Normal for large n
    • Always right-skewed with highest probability at k=1
    • Left-skewed when p is small