3. Monopoly Insurance

You are on Pacific Ave, outlined in red. An opponent owns hotels on Park Place and Boardwalk. Landing on Park Place costs you $1500; Boardwalk costs $2000.

You want to price insurance for the next roll of the two dice against landing on either of those two properties. Counting, you find that you are six steps from Park Place and eight from Boardwalk. (We set aside the issue of rolling doubles, and agree to only seek insurance on literally the next roll!)

(a) Five elementary outcomes yield a sum of six.List them.

(b) How many elementary outcomes land you on Boardwalk? List them.

(c) What is the probability you land on Park Place? Why?

(d) Complete the probability distribution assuming only Park Place and Boardwalk have non-zero monetary value.

Probability Distribution of Payout for Next Roll

Outcome Probability

2000 ?

? ?

0 ?

(e) Compute the expected value of the insurance payout.

(f) How is that value related to the long-run?

(g) Why use that expected value as a base-line for the price?

(h) If you land on Chance, you draw one out of 16 cards. One of those cards sends you to Boardwalk! What is the probability of that? Why? Hint: this involves the probability of an intersection.

THIAY CHOLTAH 1 MONOPOLY THEIAH CHANCE TAX FAT INK INCOME TAI TAHAR GO\fELECTED UP CHAIRMAN PIT IF TOO PAST GO IF TOM PASS CO, COLLET SEEM COLLECT $310 in The in COLLECT $1SO GET OUT OF JAIL FREETHE HOLE IN YOU INHERIT PAT SECOND PATTE STOCK SCHOOL TAX OF $150 BEAUTY CONTEST 145 COLLECT $10 GET PUT ADVANCE TO GO PIT HOSPITAL OF JAIL, FREE Chemanly Arit LIFE INSURANCE IMAG FUND INCOME TAX MATURES MATURES COLLECT 151 REFUND COLLECT $10 COLLECT $101 COLLECT SEO WECENE IN YOUR FAVOR DOCTOR'S FIEF PAY $10 COLLECT 9:140