A game of chance 4. You have made it to the final round of a game show. The anno

Question

A game of chance 4. You have made it to the final round of a game show. The announcer asks you the final multiple choice question, which has four possible answers, (a), (b), (c), and (d). If you answer the question correctly, you win $1,000,000. After considering the question, you realize you are not sure, but you have your suspicions. You think the answer is either choice (a) with probability 60%, or choice (b) with probability 40%. You are certain the answer is not choice (c) or (d). You have three options: . Choose not to answer the question. You walk away with $500,000 Select an answer (a or b). If you are correct, you win $1,000,000. If you are incorrect, you win only 32,000 Phone a friend. In this option, the announcer allows you to call a friend for help After listening to your friend's response, you must then answer the question. You know that: Given the correct answer is (a), your friend will say "a" with probability 80%. * Given the correct answer is (b), your friend will say "b" with probability 80%. . What is the probability that your friend says the answer is "a"? . What is the probability that your friend says the answer is "b"? Make a decision tree to find your best strategy. In words, what should your strategy be? How much money do you expect to win?

Explanation / Answer

Let the event friend saying 'a' be FA

'a' being correct answer is AC

Let the event friend saying 'b' be FB

'b' being correct answer is BC

therefore

P(FA GIVEN AC) = 0.8

P( FA/ AC) = 0.8

P (FA intersectn AC)/ P (AC) = 0.8

We know P(AC) = 0.6 and P(BC) =0.4

P (FA intersectn AC)/ 0.6 = 0.8

P (FA intersectn AC) = 0.8 * 0.6 = 0.48

The probability that the friend says 'a' is 0.48

P(FB GIVEN BC) = 0.8

P( FB/ BC) = 0.8

P (FB intersectn BC)/ P (BC) = 0.8

P(BC) =0.4

P (FA intersectn AC)/ 0.4 = 0.8

P (FA intersectn AC) = 0.8 * 0.4 = 0.32

The probability that the friend says 'b' is 0.32

Decision tree is

as seen above the best decision is giving 516000 if he selects the answer himself.

If he phones his friend then he gets only 496641

If he walks away he gets 500000

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