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  • State True or False for the statements in the Exercise. Let P(A) > 0 and P(B) > 0. Then A and B can be both mutually exclusive and independent.

State True or False for the statements in the Exercise.
Let P(A) > 0 and P(B) > 0. Then A and B can be both mutually exclusive and independent.

Answers (1)

FALSE

Events are mutually exclusive when–

P(A∪B) = P(A) + P(B)
But as per the conditions in question, it is not necessary that they will meet the condition because it might be possible that
P(A ∩ B) ≠ 0

Events are independent when–
P(A ∩ B) = P(A)P(B)
Again P(A) > 0 and P(B)> 0 are not sufficient conditions to validate them.

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infoexpert22

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