Let A and B be events with P(A)= 0.7, P(B)= 0.2, and P(A and B)= 0.15.

Question

Are A and B independent? Explain.
Compute P( A or B).
Are A and B mutually exclusive? Explain

Answer 1

To determine if events A and B are independent, we need to check if P(A and B) = P(A) * P(B).

Given: P(A) = 0.7, P(B) = 0.2, and P(A and B) = 0.15.

P(A) * P(B) = 0.7 * 0.2 = 0.14

Since P(A and B) = 0.15 is not equal to P(A) * P(B) = 0.14, events A and B are not independent.

To compute P(A or B), we can use the formula:
P(A or B) = P(A) + P(B) - P(A and B)
P(A or B) = 0.7 + 0.2 - 0.15
P(A or B) = 0.7 + 0.2 - 0.15 = 0.75

Therefore, P(A or B) = 0.75.

Events A and B are not mutually exclusive because they have a nonzero intersection. If events are mutually exclusive, they cannot occur at the same time, i.e., P(A and B) = 0. However, in this case, P(A and B) = 0.15, which means that A and B can occur simultaneously.