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A First Course in Probability | 9th Edition | ISBN: 9780321794772 | Authors: Sheldon Ross
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(a) A gambler has a fair coin and a two-headed coin in his

Chapter 3, Problem 37P

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QUESTION:

Problem 37P

(a) A gambler has a fair coin and a two-headed coin in his pocket. He selects one of the coins at random; when he flips it, it shows heads. What is the probability that it is the fair coin?

(b) Suppose that he flips the same coin a second time and, again, it shows heads. Now what is the probability that it is the fair coin?

(c) Suppose that he flips the same coin a third time and it shows tails. Now what is the probability that it is the fail-coin?

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QUESTION:

Problem 37P

(a) A gambler has a fair coin and a two-headed coin in his pocket. He selects one of the coins at random; when he flips it, it shows heads. What is the probability that it is the fair coin?

(b) Suppose that he flips the same coin a second time and, again, it shows heads. Now what is the probability that it is the fair coin?

(c) Suppose that he flips the same coin a third time and it shows tails. Now what is the probability that it is the fail-coin?

ANSWER:

Step 1 of 3

(a)

It is given that a gambler has a fair coin and a two-headed coin with him.The gambler selects a coin at random and flips it.He got head.

Using this we need to find the probability that the selected coin is a fair coin.

Let F be the event that the gambler selects the fair coin.

Let be the observations made by the gambler.

Before any observations are made, the probability that the selected coin is a fair coin becomes

0.5.

Thus, 0.5 is the probability that the selected coin is a fair coin.

 

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