Question

If A, B and C are mutually exclusive and exhaustive events and it is known that P(A U B) = 0.63, calculate P(C)​

Answer 1

Given:

A, B and C are mutually exclusive and exhaustive events and it is known that P(A U B) = 0.63

To find:

Calculate P(C)​

Solution:

From given, we have:

A, B and C are mutually exclusive and exhaustive events and it is known that P(A U B) = 0.63

P(A∪B∪C) = P(S) = 1  

P(A∩B∩C) = P(A∩B) = P(B∩C) = P(A∩C) = 0  

We know, P(A∪B∪C) = P(A) + P(B) + P(C) − P(A∩B) − P(B∩C) − P(A∩C) + P(A∩B∩C)

1 = P(A) + P(B) + P(C) − 0 − 0 − 0 + 0

1 − P(A) − P(B) = P(C)

1 − {P(A) + P(B)} = P(C)

1 − {P(A∪B) + P(A∩B)} = P(C)

1 − (0.63) = P(C)

Therefore, P(C) = 0.37