Date: Tue, 6 Apr 1999 10:42:01 EDT
Subject: Probability-Can't get it.
To: QandQ@MathCentral.uregina.ca

The probabilities of being an "instant winner" of \$25 or \$50 in a lottery are 1/600 and 1/1200, respectively. The mathematical expectation of being an "instant winner" of \$25 or \$50 is?

Hi
First you need to assume that on a single draw you can't be both a \$25 winner and a \$50 winner. You can win one or the other but not both. If it is possible to be both a \$25 and a \$50 winner on the same draw then you need more information to find the expectation.
The prob of winning \$25 is 2/1200 and the prob of winning \$50 is 1/1200. This means that, in the long run, for every 1200 tickets you buy, there are 2 that will be \$25 winners and 1 that will be a \$50 winner. So, on the average for every 1200 tickets you buy:
 2 are \$25 winners for a total winning of \$50 1 is a \$50 winner for a total winning of \$50 1197 are losers for a total winning of \$0
Thus you have a grand total winning of \$100 on 1200 tickets or an average winning of \$100/1200 = \$0.0833 per ticket. This is the expectation or expected winning, eight and one third cents.

Cheers
Jack and Penny

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