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 1 of 2
- A. 0.10
- B. 0.28
- C. 0.70
- D. 1.20
Explanation: For mutually exclusive events, the events cannot occur together, so P(A ∪ B) = P(A) + P(B).
Correct answer: 0.70- A. 3/8
- B. 5/8
- C. 3/5
- D. 5/3
Explanation: Since every ball is either red or blue, not blue means red in this bag.
Correct answer: 5/8- A. 0.400
- B. 0.625?
- C. 0.625
- D. 0.500
Explanation: Using Bayes' theorem, P(B | defective) = (0.40 × 0.05) divided by [(0.60 × 0.02) + (0.40 × 0.05)] = 0.625.
Correct answer: 0.625- A. 3/8
- B. 1/4
- C. 1/8
- D. 1/2
Explanation: This follows a binomial distribution with n = 4, p = 1/2, and r = 2. The probability is C(4,2)(1/2)^2(1/2)^2 = 6/16 = 3/8.
Correct answer: 3/8- A. 3
- B. 6
- C. 7
- D. 20
Explanation: The mean of a binomial distribution is np. Therefore, E(X) = 20 × 0.3 = 6, while 20 is the number of trials rather than the expected…
Correct answer: 6- A. 2
- B. 4
- C. 8
- D. 16
Explanation: For a Poisson distribution, both the mean and the variance equal λ. Hence, when λ = 4, the variance is also 4.
Correct answer: 4- A. 2.10
- B. 2.40
- C. 2.70
- D. 3.00
Explanation: The expected value is found by multiplying each value by its probability and adding the results: (1 × 0.2) + (2 × 0.5) + (4 × 0.3) = 2.4.
Correct answer: 2.40- A. 0.032
- B. 0.128
- C. 0.160
- D. 0.200
Explanation: The first two attempts must fail and the third must succeed. Thus, the probability is (0.8)^2 × 0.2 = 0.128, which is the geometric…
Correct answer: 0.128- A. 0.025
- B. 0.250
- C. 0.500
- D. 0.975
Explanation: The standard normal distribution is symmetric about zero, and zero is its mean and median.
Correct answer: 0.500- A. 0.10
- B. 0.30
- C. 0.55
- D. 1.10
Explanation: For independent events, the probability of their intersection equals the product of their probabilities.
Correct answer: 0.30- A. 1/6
- B. 5/18
- C. 25/36
- D. 11/36
Explanation: The probability of no six in two rolls is (5/6)^2 = 25/36. Therefore, the probability of at least one six is 1 - 25/36 = 11/36.
Correct answer: 11/36- A. 0.3
- B. 0.7
- C. 0.9
- D. 1.1
Explanation: The addition rule gives P(A ∪ B) = P(A) + P(B) - P(A ∩ B). Thus, the result is 0.5 + 0.4 - 0.2 = 0.7.
Correct answer: 0.7- A. 0.49
- B. 0.70
- C. 1.10
- D. 1.70
Explanation: The mean is E(X) = 1.1 and E(X²) = 1.7. Hence, Var(X) = E(X²) - [E(X)]² = 1.7 - 1.21 = 0.49.
Correct answer: 0.49- A. 0.1024
- B. 0.1536
- C. 0.2304
- D. 0.3456
Explanation: Use the binomial formula: C(5,3)(0.4)^3(0.6)^2. This equals 10 × 0.064 × 0.36 = 0.2304.
Correct answer: 0.2304- A. e^-1
- B. 1 - e^-3
- C. 3e^-3
- D. e^-3
Explanation: For a Poisson variable, P(X = x) = e^-λ λ^x/x!. When x = 0 and λ = 3, this becomes e^-3.
Correct answer: e^-3- A. 0.25
- B. 2
- C. 4
- D. 5
Explanation: The number of attempts until the first success follows a geometric distribution. Its expected value is 1/p, so 1/0.25 = 4 attempts.
Correct answer: 4- A. 1/6
- B. 1/3
- C. 1/2
- D. 2/3
Explanation: For a uniform distribution, probability equals the length of the required interval divided by the total length.
Correct answer: 1/3- A. 1
- B. 2
- C. 7
- D. 20
Explanation: The standardized value is z = (X - μ)/σ. Substituting the values gives z = (70 - 50)/10 = 2.
Correct answer: 2- A. Equal to its variance
- B. Always 1
- C. Equal to its mean
- D. Always 0
Explanation: For a continuous random variable, probability is assigned to intervals, not individual points.
Correct answer: Always 0- A. 0.8
- B. 4
- C. 5
- D. 20
Explanation: The standard error of the sample mean is σ divided by the square root of n. Thus, it is 20/√25 = 20/5 = 4.
Correct answer: 4Probability and Probability Distributions MCQs: common questions
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