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If A and B are two independent events such that `P(overline(A) cap B)=2//15 " and " P(A cap overline(B))=1//6`, then P(B), isA. `(1)/(5) " or ", (4)/(5)`B. `(1)/(6) " or", (5)/(6)`C. `(4)/(5) " or", (1)/(6)`D. `(5)/(6) " or", (1)/(5)` |
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Answer» Correct Answer - C Let P(A)=x and P(B)=y. Since A and B are independent events. Therefore, `P(overline(A) cap B)=2//15` `implies P(overline(A))P(B)=2//15` `implies {1-P(A)}P(B)=2//15` `implies (1-x)y=2//15` `implies y=xy=2//15` and, `P(A cap overline(B))=(1)/(6)` `implies P(A)P(overline(B))=(1)/(6)` `implies x(1-y)=(1)/(6) implies x-xy=(1)/(6)` Subtracting (i) from (ii), we get `x-y=(1)/(30) implies x=(1)/(30)+y` Putting this value of x in (i), we get `y-y ((1)/(30)+y)=(2)/(15)` `implies 30y-y-30y^(2)=4` `implies 30y^(2)-29y+4=0` `implies (6y-1)(5y-4)=0 implies y=1//6 " or ", y=4//5` `therefore P(B)=1//6 " or ", P(B)=4//5` |
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