An urn contains 3 red balls and `n`white balls. Mr. A draws two balls together from the urn. Theprobability that they have the same color is 1/2 Mr. B. Draws one balls formthe urn, notes its color and replaces it. He then draws a second ball fromthe urn and finds that both balls have the same color is 5/8. The possiblevalue of `n`is`9`b. `6`c. `5`d. 1

An urn contains 3 red balls and `n`white balls. Mr. A draws two balls

1.	An urn contains 3 red balls and `n`white balls. Mr. A draws two balls together from the urn. Theprobability that they have the same color is 1/2 Mr. B. Draws one balls formthe urn, notes its color and replaces it. He then draws a second ball fromthe urn and finds that both balls have the same color is 5/8. The possiblevalue of `n`is`9`b. `6`c. `5`d. 1
Answer» Correct Answer - 1 There are n white balls in the turn. `implies` Probability of Mr. A to draw two balls of same color is `(""^(3)C_(2)+""^(n)C_(2))/(""^(n+3)C_(2))=1/2("given")` `or (6+n(n-1))/((n+3)(n+2))=1/2` `or n^(2)-7n+6=0` `impliesn=1or6" "(1)` Also required probability for Mr. B according to the question is `(3)/(n+3)(3)/(n+3)+(n)/(n+3)(n)/(n+3)=5/8"(given)"` Solving, we get `n^(2)-10n +9=0,n=1or9" "(2)` From (1) and (2), `n=1`

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