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?
Source: Australian Olympiad 1983
(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 20181016 09:37:44 