Question

The student council is hosting a drawing to raise money for scholarships. They are selling tickets for $6 each and will sell 500 tickets. There is one $2,000 grand prize, four $300 second prizes, and fifteen $40 third prizes. You just bought a ticket. Find the expected value for your profit. Round to the nearest cent.

Answer 1

Given data:

Cost of ticket, c=$6

Total number of ticket, n=500

Grand prize, w1 = $2000

Number of grand prize, x1 = 1

Probability for getting first prize, p1 = x1/n =1/500

Expected value for getting Grand prize, E1 = p1*w1 = (1/500)*(2000)=$4

Expected value for getting first prize, E1 = $4

Second prize, w2 = $300

Number of second prize, x2=4

Probability for getting second prize , p2 = x2/n=4/500

Expected value for getting second prize, E2 = p2*w2 = (4/500)*(300)=$2.4

Expected value for getting second prize, E2 = $2.4

Third prize, w3=$40

Number of third prize , x3=15

Probability for getting third prize, p3 = x3/n=15/500

Expected value for getting third prize, E3 = p3*w3 = (15/500)*(40)=$1.2

Expected value for getting third prize, E3 = $1.2

Expected profit = (Total expected price ) -(Cost of ticket)

Expected profit = (E1+E2+E3)-(c)

Expected profit = (4+2.4+1.2)-(6)

Expected profit = (7.6)-(6) = 1.6

Expected value for profit is $1.6