25 Jul 2013

Black-Balled: Upper Secondary Mathematics Competition Question

Imagine you have two identical boxes. Inside each box are four balls; the balls are identical to the touch but seven of them are coloured white and one is black. You randomly select one box then, without looking inside, randomly pick out one ball and put it to one side. Repeat this process until one of the boxes is empty.

What is the probability that the black ball is still inside the other box?

Although physically difficult to actually play this game randomly, you could select which box to open by flipping a coin.

[Adapted from the Math Prize for Girls 2012]

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