If P(A)=0.4, P(A∪B)=0.7, then the probability of B will be maximum when A and B are: MCQ with Answer and Explanation

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If P(A)=0.4, P(A∪B)=0.7, then the probability of B will be maximum when A and B are:

A. B is a subset of A

B. Mutually exclusive

C. Independent

D. A is a subset of B

Answer: Option D

Solution (By JKExamLibrary)

P(A∪B)=P(A)+P(B)-P(A∩B). To maximize P(B) given P(A∪B)=0.7 and P(A)=0.4, set P(A∩B)=P(A)=0.4 (i.e., A⊂B). Then 0.7=0.4+P(B)-0.4 => P(B)=0.7 max.

This question belongs to: Accountancy and Statistics Statistics

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