7. Suppose you play a game with your parter. Your partner pick one card, then yo

Question

7. Suppose you play a game with your parter. Your partner pick one card, then you pick. Suppose now your parter picked two cards and you picked one. You got an Ace. Assume you know your partner got a pair of QQ, for you, you have two options. You can pick one, or just give up. If you give up, no lose no win. If you try to pick one more card to compare with your partner, from the remaining 49 cards, if you pick an another Ace, you will win 100, if you pick other card, you will lose 2. Which option you should choose? ( You need to compare the expectations for the two options to get the full points).

Explanation / Answer

A , Q , Q are gone from the pack of cards

P = Probability of picking an ace = 3/ 49 (3 aces remain in 49 cards)

Expectation in this case = P* amount = 3/49 * 100 = 300/49 = 6.122

Now , Q = Probability of not picking an ace = 1 - 3/ 49 = 46/49

Expectation in this case = Q* amount = 46/49 * (-2) = -92/49 = -1.877

Expectation in case of winning is much more than losing , therefore he should pick one more card.

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