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]
Feel free to comment, ask questions and even check your answer in the comments box below powered by
If you enjoy using this website then please consider making a donation - every little helps :-)
You can receive these questions directly to your email box or read them in an RSS reader. Subscribe using the links on the right.
Don’t forget to follow Gifted Mathematics on Google+, Facebook or Twitter. You may add your own interesting questions on our Google+ Community and Facebook..
You can also subscribe to our Bookmarks on StumbleUpon and Pinterest. Many resources never make it onto the pages of Gifted Mathematics but are stored in these bookmarking websites to share with you.