@MISC{Oza93onthe, author = {Nikunj C. Oza}, title = {On The Confusion in Some Popular Probability Problems}, year = {1993} }

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Abstract

. In this paper, we will look at three probability problems that have caused widespread disagreement and much confusion. We will look at some false solutions to these problems, the reasons why they are incorrect, and the correct solutions. We will also find a common pattern in the three problems which probably accounts for these false solutions. 1. Introduction. In a series of articles entitled "Ask Marilyn" in Parade Magazine [1], an interesting probability problem was discussed. The problem, often called the "Let's Make a Deal" Problem, was stated in the first article [1a]: "Suppose you're on a game show and given a choice of three doors. Behind one is a car; behind the other two are goats. You pick Door No. 1, and the host, who knows what's behind them, opens No. 3, which has a goat. He then asks if you want to pick No. 2. Should you switch?" Marilyn vos Savant, who is in the "Guinness Book of World Records Hall of Fame" for "Highest IQ," and author of the "Ask Marilyn" articles, r...