Free Probability and Probability Distributions MCQs with Answers
30 Probability and Probability Distributions MCQs from Quantitative Methods, each with the correct answer and a written explanation of why it is correct. Free and unlimited, with no account needed.
Probability covers sample spaces, events, complements, mutually exclusive and independent events, conditional probability, addition and multiplication rules, and tree diagrams. Distributions describe discrete random variables through probability tables, expected value and variance, including binomial and normal models where their conditions and parameters must be identified.
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30 questions · page 2 of 2
- A. 1/169
- B. 1/221
- C. 1/256
- D. 1/265
Explanation: There are 4 aces among 52 cards, so the probability of an ace first and another ace second is (4/52)(3/51) = 1/221.
Correct answer: 1/221- A. 1.6
- B. 2.0
- C. 2.4
- D. 4.0
Explanation: For a binomial variable, variance equals np(1 − p). Thus, Var(X) = 10(0.4)(0.6) = 2.4, not np, which is the expected value.
Correct answer: 2.4- A. 2e⁻²
- B. 1 − 2e⁻²
- C. e⁻²/2
- D. 4e⁻²
Explanation: The Poisson probability formula is P(X = x) = e⁻λ λˣ/x!. Substituting λ = 2 and x = 2 gives e⁻²(2²/2!) = 2e⁻².
Correct answer: 4e⁻²- A. 273/760
- B. 189/760
- C. 91/380
- D. 7/20
Explanation: This is a hypergeometric probability because selection occurs without replacement.
Correct answer: 273/760- A. 0.3413
- B. 0.5000
- C. 0.6826
- D. 0.9544
Explanation: The central interval from one standard deviation below the mean to one above the mean contains about 68.26 percent of a normal…
Correct answer: 0.6826- A. 4
- B. 6
- C. 7
- D. 10
Explanation: The mean of a uniform distribution on [a, b] is (a + b)/2. Therefore, the expected value is (4 + 10)/2 = 7.
Correct answer: 7- A. The number of trials is random
- B. Each trial has more than two outcomes
- C. The success probability changes each trial
- D. The trials are independent with fixed success probability
Explanation: A binomial model requires a fixed number of independent trials, two outcomes per trial, and a constant success probability.
Correct answer: The trials are independent with fixed success probability- A. 1/6
- B. 1/2
- C. 2/3
- D. 5/6
Explanation: The density is constant, so the probability equals the interval length multiplied by the density. Hence P(2 ≤ X ≤ 5) = (5 − 2)(1/6) = 1/2.
Correct answer: 1/2- A. 9
- B. 16
- C. 36
- D. 81
Explanation: For a linear transformation, Var(aX + b) = a²Var(X), while the constant b has no effect.
Correct answer: 81- A. Mean 36, variance 75
- B. Mean 38, variance 75
- C. Mean 36, variance 225
- D. Mean 38, variance 225
Explanation: The mean transforms as E(Y) = 3E(X) + 2 = 38. The variance is multiplied by the square of the coefficient, so Var(Y) = 3² × 25 = 225.
Correct answer: Mean 38, variance 225