**Concept Question 2 (Trinity College)**

A front page story in the *New York Times* reported a "1 in 17 trillion"
long shot, speaking of a woman who won the New Jersey lottery twice. The probability of
winning her first prize on Oct. 24 1985 was 1 in 3.2 million, and the probability of her
winning the second time, on Feb. 13 1986, was 1 in 5.2 million. Which of the following is
the best analysis of this situation?

- The probability "1 in 17 trillion" is correct because the two events are independent and so we should multiply their probabilities together to arrive at the overall probability (i.e. 3.2 million times 5.2 million equals 17 trillion)

- The probability "1 in 17 trillion" is incorrect because the two events are
*not*independent and so we should add, not multiply their probabilities together to arrive at the overall probability.

- The probability "1 in 17 trillion" is misleading because the remarkable event
in this case is that the winner of the February drawing had won previously. The
probability that
*someone*would have won both of these drawings is closer to 1 in 5.2 million, which is millions of times more that the probability 1 in 17 million.

- The probability "1 in 17 trillion" is not correct because it’s
unreasonable that something with such a small probability should ever occur.

- The probability "1 in 17 trillion" is too low because the woman bought more than one ticket for each drawing and this was not taken into account in the Times article.

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Introduction

Contributors: Barbara Walden, Judith Moran

Institution: Trinity College

Target Audience: General

7/30/99