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 Box of balls (Posted on 2018-10-16)
A box contains p white balls and q black balls. Beside the box there is a pile of black balls. Two balls are taken out from the box.
If they are of the same colour, a black ball from the pile is put into the box.
If they are of different colours, the white ball is put back into the box.
This procedure is repeated until the last pair of balls are removed from the box and one last ball is put in.

What is the probability that this last ball is white?

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 re: Half a solution (partial spoiler), finished | Comment 2 of 6 |
(In reply to Half a solution (partial spoiler) by Steve Herman)

You gave a great explanation.

This is easy to finish off.  If p is even, then when there are two balls left, they must either both be white or both be black.  On the last draw, they then match and are replaced by a black ball.

IF p IS EVEN, THEN THE LAST BALL MUST BE BLACK.

The answer to the question in the problem is

If p is odd, the probability is 1.  If p is even, the probability is 0.

Edited on October 17, 2018, 7:44 am
 Posted by Jer on 2018-10-16 09:37:44

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