3. Consider the following three games. Which one would you be most likely to pla

Question

3. Consider the following three games. Which one would you be most likely to play? Which one would you be least likely to play? Explain your answer mathematically. Game I: You toss a fair coin once. If a head appears you receive $3, but if a tail appears you have to pay $1. Game II: You buy a single ticket for a raffle that has a total of 500 tickets. Two tickets are chosen from the 500. The holder of the first ticket selected receives $300, and the holder of the second ticket selected receives $150. Game III: You toss a fair coin once. If a head appears you receive $1,000,002, but if a tail appears you have to pay $1,000,000.

Explanation / Answer

To check the most likely and least likely games i would play, we need to find the expected gain/ loss in each case.

a) P(Head) = 1/2

P(Tail) = 1/2

So,

E(Winning) = 1/2 (3) + 1/2 (-1) = 1/2 *2 = 1

b) Probability distribution will be:

Buying price of ticket is not given so i am assuming it to be $1.

Hence,

Mean = 300(1/500) + 150(1/500) - 1(498/500) = -0.096

c) P(Heads) = 1/2

P(Tails) = 1/2

E(Winning) = 1/2 * (1000002 - 1000000) = 1

So,

We can see that the expected winning is same in the case of Game I and Game III but Game III requires high amount so the game which we most likely to play is game I.

Also game II is showing expected loss instead of profit (Assuming ticket cost is $1) so this is the game we would least likely to pay.

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