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Question

If A and B are two independent events such that P(A)>0.5, P(B)>0.5, P(A¯¯¯¯B)=325, P(¯¯¯¯AB)=825, then the value of P(AB) is

A
1225
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B
1425
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C
1825
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D
2425
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Solution

The correct option is A 1225
Given : P(A¯¯¯¯B)=325,P(¯¯¯¯AB)=825
As A and B are independent events, so
P(AB)=P(A)×P(B)
Assuming P(A)=a,P(B)=b
P(A)P(AB)=325
P(A)P(A)×P(B)=325aab=325 (1)P(B)P(AB)=825P(B)P(A)×P(B)=825bab=825 (2)

From equations (1) and (2), we get
a(1825(1a))=325a(1725a)=3(1a)25a220a+3=025a215a5a+3=0(5a1)(5a3)=0a=35 (P(A)>0.5)
From equation (2), we get
b=45P(AB)=P(A)×P(B)=1225

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