Question

In another lottery, there are many winning prizes. One prize is $1000, another prize is $200, and then there are eight $10 gift cards. If each ticket costs $3 and exactly 800 tickets will be sold, find the expected net gain (expected value) if someone buys one ticket.

Answer 1

Let X is net gain if someone purchase one lottery ticket.

p(x) is probability of net gain.

Each ticket cost at $3, there are 800 tickets will be sold.

1 prize of $1000 , 1 prize of $200 and 8 gift cards of $10 each

the probability distribution of X

   x      997      197      7             -3

p(x)   1/800    1/800   8/800      790/800

So the expected gain is

E(X) =X * P(X)

E(X) = 997*(1/800) + 197*(1/800) + 7*(8/800) - 3*(790/800)

E(X) = - 1.4   or $(1.4)