Suppose Good e x a m result (E=Good) indicates e x a m scores higher than 70 poi

Question

Suppose Good e x a m result (E=Good) indicates e x a m scores higher than 70 points (out of 100). Your friend wanted to play a game with you. The rule is simple. If you get more than 70 from the e x a m tomorrow, your friend will give you $100. Otherwise, you have to give your friend $50. You know that there is no party tonight.

Using the probabilistic model above, answer the following:

Suppose you are sick and you do have a party that you have to go tonight. Also, because of your strong ego, you HAVE to play this game. Now, your friend knows about this situation and tries to earn some easy money from you. Your friend wants $50 if you lose the game but you can set the winning prize by yourself. What is the minimum prize ($) would you like to set? In other words, what is the minimum monetary prize that yields non-negative expected utility (monetary value)?

PIN Yes) PIN No) 0.8 0.2 POS Yes) P (S-No) Party Last Night 0.1 0.9 Sick (S) Hangover (H) Exam Result (E) Yes No SH PCE Good) PIE Bad) Y Y 0.1 0.9 Y N 0.5 0.5 N Y 0.6 0.4 N N 0.3 0.7 0.9 0.8 0.1 0.2

Explanation / Answer

Probaiblity of winning = P(Good/Result/Sick and party) = 0.1 (First row and first column of the table)

P(Losign) = 0.9

E(X) = 0.1* x + 0.9*(-50)

or x =450

Hence, minimum prize should be 450 dollars to give me a non-negative utility

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