Retorts

Lies, Damned Lies...

Russell Dear is wrong [Neurobics, July].

He seems to assume that the odds that the quiz participant has chosen a car (which are initially 1/3) are unchanged when the quizmaster reveals a goat behind another door.

This is wrong; the odds that he has chosen a car now immediately rise to 1/2, and the chances that there is a car behind the other door are also 1/2, so there is no point in changing.

Mr Dear is unlikely to do well in a TV quiz show. The quizmaster, who knew he had chosen a car, was obviously using a ruse to get him to change his mind, and he fell for it.

The Lewis Carroll problem is equally simple. There is an equal chance he has chosen one of the two counters. If he has chosen the first, the chances that the remainder is white are 1/1. If he chose the second, the remainder has a 1/2 chance of being white. The average of these two is a chance of 3/4.

Vincent Gray, Wellington

Perhaps the following diagram will help clarify the odds. Two goats and one car produce three possible combinations (after all, you don't care which goat you get). Assume you pick door one and the game show host picks a goat (those selections shown in black). Now can you see that it's to your advantage to change your choice?