Question

Suppose you won the Florida lottery and were offered a choice of $1,000,000 in cash or a gamble in which you would get $2,000,000 if a head were flipped but $0 if a tail came up. Show your work.

a. What is the expected value of the gamble?

b. Would you take the sure $1,000,000 or the gamble?

c. If you choose the sure $1,000,000, are you a risk averter or a risk seeker?

Answer 1

Risk Free Choice - 10,00,000

Gamble - Head - 20,00,000 Tail - 0

A) Expected value of the gamble will be the average of the money generated by multiplying the weights.

Condition 1 Head - 20,00,000

Condition 2 Tail - 0

Expected Value = W1R1 + W2R2

Where W1 is the weight of condition 1

W2 is the weight of condition 2

R1 is the return of Condition 1

R2 is the return of Condition 2

So, We know there is 50% chance of getting each head or tail.

So, W1 and W2 is 50%

Expecte Return -= 50% * 20,00,000 + 50% * 0

= 50% * 20,00,000 + 0

Expected Value= $ 10,00,000

Part B) The risk free option will be choosen because you are getting it for sure and the expected value of the gamble is also the same with more risk involved in it.

Part C) If we take $1,000,000 for sure than it would be risk avert, because it refers to the individual who doesn't take risk or reluctant to take risk. In $10,00,000 cash there is no risk involvement while in gamble there is risk of getting it zero, So, It would be risk averse.