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Elementary Statistics: A Step By Step Approach | 9th Edition | ISBN: 9780073534985 | Authors: Allan Bluman
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Con Man Game Consider this problem: A con man has 3 coins.

Chapter 4, Problem 1CTC

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QUESTION:

Consider this problem: A con man has 3 coins. One coin has been specially made and has a head on each side. A second coin has been specially made, and on each side it has a tail. Finally, a third coin has a head and a tail on it. All coins are of the same denomination. The con man places the 3 coins in his pocket, selects one, and shows you one side. It is heads. He is willing to bet you even money that it is the two-headed coin. His reasoning is that it can’t be the two-tailed coin since a head is showing; therefore, there is a 50-50 chance of it being the two-headed coin. Would you take the bet?

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QUESTION:

Consider this problem: A con man has 3 coins. One coin has been specially made and has a head on each side. A second coin has been specially made, and on each side it has a tail. Finally, a third coin has a head and a tail on it. All coins are of the same denomination. The con man places the 3 coins in his pocket, selects one, and shows you one side. It is heads. He is willing to bet you even money that it is the two-headed coin. His reasoning is that it can’t be the two-tailed coin since a head is showing; therefore, there is a 50-50 chance of it being the two-headed coin. Would you take the bet?

ANSWER:

Step 1 of 2:

It is given that a man has 3 coins.One coin has heads on both the sides.Another coin has tails on both the sides.The third coin has head on one side and tail on another side.

The man places the three coins in his pocket and selects one and shows its one side and it is head.

So, he bets even money that the selected coins is a two headed coin.There is 50-50 chance of being a regular coin or a two headed coin.

Using this we need to decide whether we need to take the bet or not.

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