Question

Consider a game in which a coin will be flipped three times. For each heads you will be paid $100. Assume that the coin comes up heads with probability 1/3. a. Construct a table of the possibilities and probabilities in this game. Probability Outcome Possibilities 0 heads, 3 tails / 1 heads, 2 tails 2 2 heads, 1 tails 3 3 heads, 0 tails b. Compute the expected value of the game. The expected value of the game is $ c. How much would you be willing to pay to play this game? a person who is risk-neutral will be willing to pay $ A person who is risk averse will want to pay less than $ d. Consider the effect of a change in the game so that if tails comes up two times in a row, you get nothing. How would your answers to the first three parts of this question change? Payoff outcome Possibilities Probability 3 tails, 0 heads taile, heads, tails tails, tails, heada 2 heads, tails, tails 2 heads, 1 taiis 3 heads, 0 tails Expected value $ a person who is risk- neutral will be willing to pay $ A person who is risk-averse will want to pay less than S

Answer 1

Solution

(A)

Given probability or getting a head = 2/3

probability of getting a tail=4-2/3=4/3.

Probability Possibilities outcome 1/27 1 0 heads, 3 tails 2/9 2 1 heads, 2 tails 3 4/9 2 heads, 1 tails 4 8/27 3 heads, 0 tails st

(B)

As $ 100 will be paid for each head,

Expected value = 1/27 * ($ 0)+ 2/9 * ($ 100)+ +4/9 * ($ 200) + 8/27 * ($300)

$= 200

(C)

A person who is risk averse will want to pay less then $ 200

a person who is risk neutral will be willing to pay $ 200

(D)

Probability Possibilities Outcome Payoffs 1 1/27 3 tails, O heads 2/27 $100 2 tails, heads, tails 2/27 3 tails, tails, heads 2/27 heads, tails, tails 4 $ 200 5 4/9 2 heads, 1 tails 8/27 $ 300 3 heads, 0 tails LO

Expected value = 1/27* ($ 0)+2/27*($ 100)+2/27*($ 0) + 2/27 * ($ 0)+ 4/9 * ($ 200)+8/27* ($ 300 )

= $ 185.

Thank you..