InterviewSolution
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InterviewSolution
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If ` 0 lt P(A) lt 1, 0 lt P(B) lt 1` and `P(A cup B)=P(A)+P(B)-P(A)P(B)`, thenA. `P(A//B)=P(A)+P(B)`B. `P(A cup B)^(c )=P(A^(c ))P(B^(c ))`C. `P(A^(c )-B^(c ))=P(A^(c ))P(B^(c ))`D. `P(B//A)=P(B)-P(A)` |
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Answer» Correct Answer - B We have, `P(A cup B)=P(A)+P(B)-P(A)P(B)` `implies P(A)+P(B)-P(A cap B)=P(A)+P(B)-P(A)P(B)` `implies P(A cap B)=P(A)P(B)` `implies` A and B are independent events `implies A^(c ) " and " B^(c )` are independent events `implies (A^(c ) cap B^(c ))=P(A^(c ))P(B^(c ))` `implies P(A cup B)^(c ) =P(A^(c ))P(B^(c ))` Hence, option (b) is true. |
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