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