The Car and the Goats
1992; Taylor & Francis; Volume: 99; Issue: 1 Linguagem: Inglês
10.2307/2324540
ISSN1930-0972
Autores Tópico(s)Teaching and Learning Programming
Resumo1. THE PROBLEM. A TV host shows you three numbered doors, one hiding a car (all three equally likely) and the other two hiding goats. You get to pick a door, winning whatever is behind it. You choose door #1, say. The host, who knows where the car is, then opens one of the other two doors to reveal a goat, and invites you to switch your choice if you so wish. Assume he opens door #3. Should you switch to #2? I'll call this Game I. It appeared in the Ask Marilyn column in Parade (a Sunday supplement) [4(a)]. Marilyn asserted that you should switch, arguing that the probability of winning, originally 1/3, had now gone up to 2/3. (Marilyn is standard terminology.) This led to an uproar featuring thousands of letters, nine-tenths of them insisting that with door # 3 now eliminated, #1 and #2 were equally likely; even the responses from college faculty voted her down two to one [4(b, c), 3]. There is no denying that the problem is tricky (even though, technically speaking, it involves only undergraduate mathematics). The purpose of this article is to unravel it all.
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