Question

1)Three independent reviewers are reviewing a book. let A₁ denote the event that a favorable review is submitted by reviewer, I = 1, 2, 3. Assume that A₁, A₂, and A₃ are mutually independent and that P(A₁) = 0.6, P(A₂) =0.57, and P(A₃) = 0.4.

a) Compute the probability that at least one of the reviewers submit a favorable review.

b) Compute the probability that exactly two reviewers submit favorable reviews.

Answer 1

Solution:

Given information:

A1, A2 and, A3 are mutually independent. it means:

A)

The probability that at least one of the reviewers submit a favorable review can be calculated as:

Therefore, the probability that at least one of the reviewers submit a favorable review is 0.90

B)

The probability that exactly two reviewers submit favorable reviews can be can calculate as:

Therefore, the probability that exactly two reviewers submit favorable reviews is 0.81