Q. 100

State True or False for the statements in the Exercise.

If A and B are independent events, then P(A′ B) = 1 – P (A) P(B′)

Answer :

TRUE

If A and B are independent events. It implies-


P(A B) = P(A)P(B)


P(A′ B) = P(A’) + P(B) – P(A’ B)


and P(A′ B) represents the probability of event ‘only B’ excluding common points.



From Venn diagram we can see:


P (A′ B) = P(B) – P (A B)


P (A′ B) = P(A’) + P(B) – P(B) + P (A B)


P (A′ B) = 1 – P(A) + P(A)P(B) {independent events}


P(A′ B) = 1 – P(A){1 – P(B)}


P(A′ B) = 1 – P(A)P(B’) …proved


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