lottery expected value

lottery expected value

Need help on statistics question.. 10 points if u can help thanks?

Say you buy 1 ticket for $1 out of a lottery of 1,000 tickets where the prize for the one winning ticket is $500. what is your expected value?
A. 1.0
B. 0.5
C. 0
D.-0.5

for any discrete random variable the expectation is:

E(X) = μ = ∑x * P(X = x)

Let X be the winnings

E(X) = (500 – 1) * 1/1000 + -1 * 999/1000
= -0.50

you expect to lose $0.50 in this lottery.