Question

The following notice appeared in the golf shop at a Myrtle Beach, South Carolina, golf course. Take into account the price of the ticket.

John Underpar buys a ticket.

a. What are Mr. Underpar's possible monetary outcomes?

Either wins the driver (worth $295) or has a worthless ticket (worth -$5)

Either wins the driver (worth $300) or has a worthless ticket (worth $0)

c. Summarize Mr. Underpar's "experiment" as a probability distribution.

d. What is the mean or expected value of the probability distribution?

e. If all 80 tickets are sold, what is the expected return to the club?

Answer 1

a. What are Mr. Underpar 's possible monetary outcomes.

Outcome 1 : buys ticket $5 and wins the driver (worth $300). Net worth = Value of driver - ticket cost = 300-5=$295

Outcome 2 : Buys ticket $5 and does not win driver. Net worth = -$5

Ans : Either wins the driver worth($295) of has a worthless ticket (-$5)

c. Summarize Mr.Underpar's "experiment" as probability distribution.

Number of ticket sold = 80

Number of tickets Mr. Underpar has purchased =1

Probability of Mr. Underpar winning the driver = Number of tickets Mr. Underpar has purchased/Total number of tickets = 1/80

Probability of Mr. Underpar not winning the driver = 1-Probability of Mr. Underpar winning the driver = 1-1/80 = 79/80

	P(x): probability
Winning nothing	79/80
Winning driver	1/80

E(X) = $\small \Sigma$ xP(x)
d. What is mean or expected value of the probability distribution.

	P(x): probability	P(x)	x: Monetary outcome	x.P(x)
Winning nothing	79/80	0.9875	-5	-4.9375
Winning driver	1/80	0.0125	295	3.6875
			Total	-1.25

mean or expected value of the probability distribution = -$1.25

Expected return

-$1.25

d.If all 80 tickets are sold, what is expected return to the club.

Money got from 80 tickets sold = 80x$5 = $400

Price of the driver = $300

Return to the club = Money got from 80 tickets sold - Price of the driver = $400 -$300=$100

When all 80 tickets are sold, expected return to the club $100

Expected return

$100