Question

Casinos in Atlantic City are looking to offer a special coin flip game where the player wins $4,000 if the coin comes up heads and loses $1,000 if the coin comes up tails. Assume a fair coin is used. Which statement below BEST describes the new coin flip game?

A. All statements are true.

B. A risk averse person would pay less than $1,500 to play this game.

C. A risk neutral person would be willing to pay $1,500 to play this game.

D. A risk seeking person would be willing to pay more than $1,500 to play the game.

E. The expected value of the game is that the participant wins $1,500.

Answer 1

As the event is a coin toss, the probability of head = Probability of toss = 1/2 = 0.5

Winning amount = $ 4000

Losing amount = - 1000

Expected value of the game = 1/2* 4000 - 1/2 * 1000 = $ 1,500

A risk averse person would be willing to pay less than $ 1500 to play the game as his certainty equivalent needs to be less than the expected value

Simiarly, A risk neutral person would be willing to pay exactly $ 1500 to play the game and risk loving person would not mind paying more than $1500 as his/her concern is only to maximise the gains.

Answer is A. All statements are true.