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An urn contains 15 white and 21 black balls. Balls are drawn one by one, without...

An urn contains 15 white and 21 black balls. Balls are drawn one by one, without replacement, until 6 white balls are drawn. Find an expression for the probability that the total number of balls drawn is x.

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Answer #1

The probability(p) of drawing a white ball

For the total number of balls drawn to be x, there should be 5 white balls among the first x-1 balls that are drawn.

Number of ways of selecting 5 white balls among x-1 balls is

No. of black balls among the first x-1 balls

The total probability of selecting 5 white balls and x-6 black balls among the first x-1 balls and then selecting a white ball in draw

Hence, the expression for the probability that the total number of balls drawn is x

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