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A box contains five balls, two are drawn at random and are found to be white. If probability of all balls in urn are white is $k$ then the value of $k$ is--

I tried by letting $y$ denote the number of white balls in the urn.Then the given problem is equivalent to $$P(\text{all balls white}|\text{two balls white})P(\text{two balls white})=P(\text{two balls white}|\text{all balls white})P(\text{all balls white})$$

Now $$P(\text{two balls white})=\frac{\binom{y}2}{\binom52}$$.Also $$P(\text{two balls white}|\text{all balls white})=1$$ And $$P(\text{all balls white})=k$$ Also $$P(\text{all balls white}|\text{two balls white})=\frac{y-2}{3}$$.I cannot however figure out how to eliminate $y$ and find out $k$.I am in search of a analytical answer which uses conditional probability. Any ideas? Thanks.

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    How did you evaluate the last conditional probability? – 2017-02-16
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    See this related problem: http://math.stackexchange.com/questions/339782/probability-that-the-bag-contains-all-balls-white-given-that-two-balls-are-white – 2017-02-16

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