Events E and F are such that P(not E or not F) = 0.25, State whether E and F are mutually exclusive.

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Solution

Given, E and F are two events such that P( not E or not F )=0.25.

According to given information.

P( not E or not F )=0.25 P( E ′ ∪ F ′ )=0.25 P ( E∩F ) ′ =0.25

Solve further.

P( E∩F )=1−P ( E∩F ) ′ =1−0.25 =0.75 P( E∩F )≠ϕ

Thus, E and F are not mutually exclusive events.

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