Question

A lottery has a grand prize of $120,000, three runner-up prizes of $24,000 each, six third-place prizes of $3000 each, and eighteen consolation prizes of $600 each. If 480,000 tickets are sold for $1 each and the probability of any one ticket winning is the same as that of any other ticket winning, find the expected net winnings on a $1 ticket. (round your answer to two decimal places.) $=

Answer 1

Answer:

$0.04

Step-by-step explanation:

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.

A fast way to check the calculation is to assume we bought all the tickets, with an outlay of $1000000. The total of prizes is 10000+10*1000+100*100+1000*10=40000

So the expectation is also 40000/1000000=$0.04