Question

EXPECTED VALUE

A $1 lottery ticket offers a grand prize of $10,000; 10 runner-up prizes each pay $1000; 100 third-place prizes each pay $100; and 1,000 fourth-place prizes each pay $10. Find the expected value of entering this contest if 1 million tickets are sold.

Answer 1

The mathematical formula to calculate expected value is
E[X]=ΣXi*p(xi)
where
E[X] is the expected value
xi is the ith outcome
P(xi) is the probability of getting the ith outcome.

Here:
x1=10000, p(x1)=1/1000000, x1*p(x1)=10000/1000000
x2=1000, p(x2)=10/1000000, x2*p(x2)=10000/1000000
x3=100, p(x3)=100/1000000, x3*p(x3)=10000/1000000
x4=10, p(x4)=1000/1000000, x4*p(x4)=10000/1000000

If we add up the products, we get 4*10000/1000000=4/100=$0.04 which is the expected value.