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Box of balls (Posted on 2018-10-16) Difficulty: 2 of 5
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

  Submitted by Ady TZIDON    
Rating: 4.0000 (1 votes)
Solution: (Hide)
None of the allowed transactions changes the parity of white balls.
Therefore last ball cannot be white if p is even, and must be white if odd.
Answer: 1 if p is odd, 0 if even.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
yes, finallySteven Lord2018-10-19 09:01:18
re(3): Half a solution (partial spoiler), finishedJer2018-10-17 07:45:02
SolutionsolutionCharlie2018-10-16 11:33:43
re(2): Half a solution (partial spoiler), finishedSteve Herman2018-10-16 11:12:52
re: Half a solution (partial spoiler), finishedJer2018-10-16 09:37:44
Half a solution (partial spoiler)Steve Herman2018-10-16 09:08:43
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