SOLUTION: A bag has 3 red and k white marbles, where k is an (unknown) positive integer. Two of the marbles are chosen at random from the bag. If the probability that the two marbles are the

Question 394011: A bag has 3 red and k white marbles, where k is an (unknown) positive integer. Two of the marbles are chosen at random from the bag. If the probability that the two marbles are the same color is 1/2, find k.
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
We assume that , or else the event of getting 2 white marbles is excluded.
The probability of getting 2 red marbles =
The probability of getting 2 white marbles =
Hence

<==> after simplifying.
<==>
<==> , after cross-multiplying and simplifying.
<==> (k-1)(k - 6) = 0.
==> k = 1, 6.
Therefore k = 6, the number of white marbles.
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