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An urn contains 3 red balls an...

# An urn contains 3 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 balls form the urn, notes its color and replaces it. He then draws a second ball from the urn and finds that both balls have the same color is 5/8. The possible value of n is 9 b. 6 c. 5 d. 1

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There are n white balls in the turn. <br> implies Probability of Mr. A to draw two balls of same color is <br> (""^(3)C_(2)+""^(n)C_(2))/(""^(n+3)C_(2))=1/2("given") <br> or (6+n(n-1))/((n+3)(n+2))=1/2 <br> or n^(2)-7n+6=0 <br> impliesn=1or6" "(1) <br> Also required probability for Mr. B according to the question is <br> (3)/(n+3)(3)/(n+3)+(n)/(n+3)(n)/(n+3)=5/8"(given)" <br> Solving, we get n^(2)-10n +9=0,n=1or9" "(2) <br> From (1) and (2), n=1
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