Part I. 40 points. · $3.1: #s 2, 4, 6, 10, 15 · $3.2: #s 1, 2, 4, 6, 8, 10, 11,

Question

Part I. 40 points. · $3.1: #s 2, 4, 6, 10, 15 · $3.2: #s 1, 2, 4, 6, 8, 10, 11, 13, 14 Part II. 40 points. 1. (10 pts.) Let's play a game... I will ask you one or two questions. You get to pick the order in which I ask you. If you get the first one correct, I will ask you the other question. If you get the first one wrong, you lose, game over. If you get the first one right, you get a prize, game continues. If you get the second one right, you get a prize again, game over If you get the second one wrong, you don't get another prize, game over. Let's call the 2 questions #1, #2. (But you get to pick their order.) Let F,Po be the probability of getting #1, #2 correct, respectively. Let Vi, be the prizes you win (in dollars) if you get #1, #2 correct, respectively. How should you decide the order in which to ask the questions? Which order maximizes the expectation? . (10 pts.)

Explanation / Answer

The event trees are

I question right -- prize and II qn                                                               

                   wrong -- lose and game over

II question-- right -- prize and gameover   

-- wrong -- lose and game over

P1 = getting 1 right

P2 = getting 2 right

The sample space = (first qn right and second wrong, first right and second right, first wrong)

Prob = P1(1-p2), P1P2, (1-P1)

Win    1 3    0

P*win P1(1-P2) 3P1P2 0

E(win) = P1-P1P2 +3P1p2 = P1+2P1P2

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If II question is asked first

E(win) = P2+2P1P2

From the person who conducts the game, if P1>P2, it is better to ask second question first.

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