In a card game, the dealer distributes one card to each player. Each player then bets an amount on his card without looking at his card. After betting, the player shows his card. If the card is an ace, the dealer pays the player five times his bet. If the card is a king, the dealer pays the player four times his bet. If the card is a queen, the dealer pays the player three times the bet. If the card is any other card, the player has to forfeit his bet. If Mr. Crap Baggins is joining the game with Rs. 13000, how much money can he hope to have, when he leaves the game?Choices:- 14000 12000 13860 15540
Question
In a card game, the dealer distributes one card to each player. Each player then bets an amount on his card without looking at his card. After betting, the player shows his card. If the card is an ace, the dealer pays the player five times his bet. If the card is a king, the dealer pays the player four times his bet. If the card is a queen, the dealer pays the player three times the bet. If the card is any other card, the player has to forfeit his bet. If Mr. Crap Baggins is joining the game with Rs. 13000, how much money can he hope to have, when he leaves the game?Choices:- 14000 12000 13860 15540
Solution
The answer to this question requires some assumptions. We need to assume that the deck of cards is a standard 52-card deck, and that the game is fair, meaning that each card has an equal chance of being drawn.
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First, let's calculate the probability of drawing each type of card. There are 4 aces, 4 kings, 4 queens, and 40 other cards in a deck. So, the probability of drawing an ace is 4/52 = 0.076923, a king is 4/52 = 0.076923, a queen is 4/52 = 0.076923, and any other card is 40/52 = 0.76923.
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Next, let's calculate the expected return for each type of card. If Mr. Crap Baggins bets Rs. 1, he can expect to win 510.076923 = Rs. 0.384615 for an ace, 410.076923 = Rs. 0.307692 for a king, 310.076923 = Rs. 0.230769 for a queen, and lose 110.76923 = Rs. 0.76923 for any other card.
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Adding these expected returns together, we find that Mr. Crap Baggins can expect to lose Rs. 0.153846 for each Rs. 1 he bets.
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If Mr. Crap Baggins starts with Rs. 13000 and bets all his money, he can expect to have 13000 - 0.153846*13000 = Rs. 11000 when he leaves the game.
So, the closest answer to the choices given is Rs. 12000.
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