A person buys a single ticket, what will their expected net gain be?

Question

A lottery consists of 5,000 tickets of $ 10 each. 4000 tickets only were sold and among them are: 300 tickets which bring 50 $ each; 200 tickets that bring $ 100 each and 100 tickets that bring $ 150 each. A person buys a single ticket, what will their expected net gain be?

Answer 1

The total expected value is the sum of the expected value for hitting each of the three rewards. Subtract the ticket price and that's the net gain.

Presumably, there are 4000 tickets in the pool.

Expected value of hitting $50 = (300/4000) * $50 = $3.75

Expected value of hitting $100 = (200/4000) * $100 = $5.00

Expected value of hitting $150 = (100/4000) * 150 = $375

Total is $12.50 - $10.00 = $2.50

Hope this helps!