Paradox Probability Puzzle Solution - 21 October
This is a famous paradox which has caused a great deal of argument and disbelief from many who cannot accept the correct answer. Four balls are placed in a hat. One is white, one is blue and the other two are red. The bag is shaken and someone draws two balls from the hat. He looks at the two balls and announces that at least one of them is red. What are the chances that the other ball he has drawn out is also red?
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Solution
There are six possible pairings of the two balls withdrawn, RED+RED, RED+WHITE, WHITE+RED, RED+BLUE, BLUE+RED, WHITE+BLUE. We know that the WHITE + BLUE combination has not been drawn. This leaves five possible combinations remaining. Therefore the chances that the RED + RED pairing has been drawn are 1 in 5. Many people cannot accept that the solution is not 1 in 3, and of course it would be, if the balls had been drawn out separately and the color of the first ball announced as red before the second had been drawn out. However, as both balls had been drawn together, and then the color of one of the balls announced, then the above solution, 1 in 5, must be the correct one.