the student council is hosting a drawing to raise money for scholarships. they are selling tickets for $10…

the student council is hosting a drawing to raise money for scholarships. they are selling tickets for $10 each and will sell 500 tickets. there is one $3,000 grand prize, two $300 second prizes, and twelve $40 third prizes. you just bought a ticket. find the expected value for your profit. round to the nearest cent.

the student council is hosting a drawing to raise money for scholarships. they are selling tickets for $10 each and will sell 500 tickets. there is one $3,000 grand prize, two $300 second prizes, and twelve $40 third prizes. you just bought a ticket. find the expected value for your profit. round to the nearest cent.

Answer

Explanation:

Step1: Define outcomes and profits

Grand prize: $3000 → profit $2990 (1 ticket) Second prize: $300 → profit $290 (2 tickets) Third prize: $40 → profit $30 (12 tickets) No prize: profit -$10 (485 tickets) Total tickets: 500

Step2: Calculate probabilities

Grand: 1/500, Second: 2/500, Third: 12/500, No prize: 485/500

Step3: Compute expected value

EV = (1/500)(2990) + (2/500)(290) + (12/500)(30) + (485/500)(-10)

Step4: Sum terms

= 5.98 + 1.16 + 0.72 - 9.7 = -1.84

Answer:

-1.84