Question

Due tri 03/13/2020 11:59 pm The student council is hosting a drawing to raise money for scholarships. They are selling tickets for $10 each and will sell 900 tickets. There is one $1,000 grand prize, two $500 second prizes, and fifteen $20 third prizes. You just bought a ticket. Find the expected value for your profit. Round to the nearest cent. Hint: Hint Video on Expected Value 2 Points possible: 1 Unlimited attempts.

Answer 1

Number of tickets sold = 900

Price of the ticket = $10

X: Profit = Value of the prize - ticket price

Number of grand prize = 1 ; Value of the grand prize = $1000 : X = 1000-10 =990

Number of second prized =2 ; Value of the second prize = $500 X = 500-10 = 490

Number of third prize = 15 ; Value of the third prize = $20 ; X = 20-10=10

That is (1+2+15) 18 tickets will get prize ; Remaining : 900-18 = 882 tickets will not get any prize

IF no prize is won profit : X = -10

Probability of getting a grand prize : P(X=990) = 1/900

Probability of getting a second prize :P(X=490) = 2/900

Probability of getting a third prize ;P(X=10) = 15/900

Probability of getting no prize : P(X=-10) = 882/900

Expected value of your profit = E(X)

E(X) = ΣXP(X) = 990 x 1/900 + 490 x 2/900 + 10 x 15/900 +(-10) x 882/900 6700 990 + 980 + 150 - 8820 900 900 = -7.44

Expected value of your profit = -$7.44

Answer:

$-7.44