A lottery offers 1 $1000 prize and 5 $100 prizes. 1000 tickets are sold. Find the expectation if a p

A lottery offers 1 $1000 prize and 5 $100 prizes. 1000 tickets are sold. Find the expectation if a person buys 1 ticket for $5.

Set up the expected values E(x):

for the 1,000 price:
E(x) = (1000 - 5) * 1/1000 = 995/1000

For the 5 $100 prizes:
E(x) = (100 - 5) * 5/1000 = 475/1000

For the losing ticket. With 6 winning tickets, we have 1000 - 6 = 994 losing tickets:
E(x) = -3 * 994/1000 = -2982/1000

We get our total expected value by adding all of these expected values up. Since they all have the same denominator, we add numerators:
E(x) = (995 + 475 - 2982)/1000
E(x) = -1512/1000
E(x) = -1.51