InterviewSolution
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InterviewSolution
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A box `B_1`, contains 1 white ball, 3 red balls and 2 black balls. Another box `B_2`, contains 2 white balls, 3 red balls and 4 black balls. A third box `B_3`, contains 3 white balls, 4 red balls and 5 black balls.A. `(116)/(181)`B. `(126)/(181)`C. `(65)/(181)`D. `(55)/(181)` |
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Answer» Correct Answer - D Let `E_(i)(i=1,2,3)` denote the event of selecting `i^(th)` bag and A denote the event of drawing one white and one red ball. Then, `P(E_(1))=P(E_(2))=P(E_(3))=(1)/(3)` `P(A//E_(1))=(1)/(6)xx(3)/(6)+(3)/(6)xx(1)/(5)=(1)/(5)` `P(A/E_(2))=(2)/(9)xx(3)/(8)+(3)/(9)xx(2)/(8)=(1)/(6)` `P(A//E_(3))=(3)/(12)xx(4)/(11)+(4)/(12)xx(3)/(11)=(2)/(11)` Required probability `=P(E_(2)//A)` `=(P(E_(2))P(A//E_(2)))/(P(E_(1))P(A//E_(1))+P(E_(2))P(A//E_(2))+P(E_(3))P(A//E_(3)))` `((1)/(3)xx(1)/(6))/((1)/(3)xx(1)/(5)+(1)/(3)xx(1)/(6)+(1)/(3)xx(2)/(11))=(55)/(181)` |
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