Statistics Probability & Distributions 1 — Questions and Answers
Question 1: If P(A) = 0.4 and P(B) = 0.3 and A and B are mutually exclusive, what is P(A or B)?
- 0.7 (Correct answer)
- 0.12
- 0.58
- 1.0
Correct answer: 0.7
For mutually exclusive events, P(A or B) = P(A) + P(B) = 0.4 + 0.3 = 0.7.
Question 2: What is the expected value of a fair six-sided die roll?
- 3.5 (Correct answer)
- 3
- 4
- 2.5
Correct answer: 3.5
The expected value is (1+2+3+4+5+6)/6 = 21/6 = 3.5.
Question 3: Which probability distribution is appropriate for modeling the number of successes in a fixed number of independent trials?
- Binomial distribution (Correct answer)
- Normal distribution
- Poisson distribution
- Uniform distribution
Correct answer: Binomial distribution
The binomial distribution models successes in a fixed number of independent Bernoulli trials with constant probability.
Question 4: What does it mean for two events A and B to be independent?
- P(A|B) = P(A) (Correct answer)
- P(A and B) = 0
- P(A or B) = 1
- P(A) = P(B)
Correct answer: P(A|B) = P(A)
Events are independent when the occurrence of one does not change the probability of the other.
Question 5: The Poisson distribution is typically used to model which type of event?
- Count of rare events occurring in a fixed interval (Correct answer)
- Proportion of successes in a sample
- Continuous measurements from a population
- Differences between two group means
Correct answer: Count of rare events occurring in a fixed interval
The Poisson distribution models the number of times a rare event occurs in a fixed time or space interval.
Question 6: What is the complement rule in probability?
- P(A') = 1 − P(A) (Correct answer)
- P(A') = P(A)
- P(A') = P(A) × P(B)
- P(A') = P(A) + P(B)
Correct answer: P(A') = 1 − P(A)
The complement of an event A contains all outcomes not in A, and their probabilities sum to 1.
Statistics Probability & Distributions 1
If P(A) = 0.4 and P(B) = 0.3 and A and B are mutually exclusive, what is P(A or B)?