If A and B are two independent events such that P(A)>0.5,P(B)>0.5, P(A∩¯¯¯¯B)=325,P(¯¯¯¯A∩B)=825, then the value of P(A∩B) 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 A1225 Given : P(A∩¯¯¯¯B)=325,P(¯¯¯¯A∩B)=825 As A and B are independent events, so P(A∩B)=P(A)×P(B) Assuming P(A)=a,P(B)=b Therefore, P(A)−P(A∩B)=325⇒P(A)−P(A)×P(B)=325⇒a−ab=325⋯(1)P(B)−P(A∩B)=825⇒P(B)−P(A)×P(B)=825⇒b−ab=825⋯(2) From equations (1) and (2), we get a(1−825(1−a))=325⇒a(17−25a)=3(1−a)⇒25a2−20a+3=0⇒25a2−15a−5a+3=0⇒(5a−1)(5a−3)=0⇒a=35(∵P(A)>0.5) From equation (2), we get ⇒b=45∴P(A∩B)=P(A)×P(B)=1225