Question

There are X, Y and Z coins in a box. X is a fair coin; Y is a coin with tail on both sides and Z is a coin with a probability of 2/5 of the head. Let's imagine we pulled a random coin out of the box. Since it is known that it is tail, what is the probability that this money will be X?

A. 1/3

B. 7/10

C. 5/21

D. 3/5

Answer #1

X is a fair coin

Let px = P(getting a tail on X)

px = 1/2 (1 out of 2 options head or tail)

Y has tail on both sides

Let py = P(getting a tail on Y)

py = 1 (2 out of 2 options which are tail)

Z has a probability of 2/5 as head

Let pz = P(getting a tail on Z)

pz = 1 - 2/5 = 3/5

Probaility of picking any coin = 1/3

Thus

pt = probability of getting a tail

To find P(coin is X given that it is a tail)

= P(coin is X | it is a tail)

= P(coin is X and it is a tail) / P(it is a tail)

= (1/3*px) / pt

Answer :

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Conditioned on the identity of the coin, the two tosses are
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Define the following events:
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