Need help plz......another statistics problem......ASAP?

Question

Plese explain the process so I can understand.
As part of a promotional scheme, the manufacturer of a new breakfast food offers a prize of $500,000 to some person willing to ry a new product distributed without charge and send in his or her name on the packaging label. The winner will be drawn at random. What is the mathematical expectation if 2,500,000 persons send in their names? Do you think it was worth the $0.39 postage? Thanks 4 ur help.

Answer 1

The probability of winning is 1 in 2,500,000
The probability of losing is 2,499,999 in 2,500,000
The prize for winning is 500,000
The "prize" for losing is 0

So your expected value is SUM of Prize*Probability of that prize
E(X) = (1/2,500,000)*500,000 + (2,499,999/2,500,000)*0
= 500,000/2,500,000 = 1/5 = 0.20

Your expected payout is then 0.20 which is less than the 0.39 for postage, so in a sense you are better off not wasting your 0.39.