Statistics Probability & Distributions

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)?

Accepted Answer

0.7

Answer

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?

Accepted Answer

3.5

Answer

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?

Accepted Answer

Binomial distribution

Answer

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?

Accepted Answer

P(A|B) = P(A)

Answer

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?

Accepted Answer

Count of rare events occurring in a fixed interval

Answer

The Poisson distribution models the number of times a rare event occurs in a fixed time or space interval.

Statistics Practice Test