Question

Given P(A) = 0.37, P(B) 0.38, and P(A or B) 0.27, are events A and B mutually exclusive? Yes, they are mutually exclusive No, they are not mutually exclusive

Answer 1

No, they are not mutually exclusive.

Explanation:

Two events are called mutually exclusive they are independent to each other.

Also, If A and B are any two events,

Then they are called mutually exclusive,

If P(A ∪ B ) = P(A) + P(B)

Or P ( A or B ) = P(A) + P(B)

Here, P(A) = 0.37, P(B) = 0.38 and P(A or B) = 0.27

Since,

0.27 ≠ 0.37 + 0.38

⇒ P ( A or B ) ≠ P(A) + P(B)

Hence, A and B are not mutually exclusive.