InterviewSolution
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InterviewSolution
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An urn contains three red balls and n white balls. Mr. A draws two balls together from the urn. The probability that they have the same color is `1//2.` Mr.B draws one ball from the urn, notes its color and rplaces it. He then draws a second ball from the urn and finds that both balls have the same color is `5//8.` The value of n is ____.A. 9B. 6C. 5D. 1 |
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Answer» Correct Answer - D In the first case, the urn contains 3 red and n white balls. The probability that color of both the balls matches is `(""^(3)C_(2)+""^(n)C_(2))/(""^(n+3)C_(2))=1/2` `or(6+n(n-1))/((n+3)(n+2))=1/2` `or2(n^(2)-n+6)=n^(2)+5n+6` `orn^(2)-7n+6=0` `impliesn=1 or 6" "(1)` In the second case, `(3)/(n+3)(3)/(n+3)+(n)/(n+3)(n)/(n+3)=5/8` Solving, we get `n^(2)-10n +9=0" "(2)` `implies n=9 or 1. From Eqs. (1) and (2), we have n=1. |
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