A purse contains 2 six sided dice. One is a normal fair die, while the other has 2 ones, 2 threes and 2 fives. A die is picked up and rolled. Because of some secret magnetic attraction of the unfair die, there is 75% chance of picking the unfair die and 25% chance of picking a fair fie. The die is rolled
and shown up the face 3. The probability that a fair die was picked up, is

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1/4

1/6

1/7

1/24

answer is A.

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Detailed Solution

P(N)=P(Normal die)= $\frac{25}{100} = \frac{1}{4}$

P(B)=P(baised die)= $\frac{75}{100} = \frac{3}{4}$

E= getting 3

P(E/N)=1/6,P(E/B)=2/6=1/3

$P (N / E) = \frac{P (N) P (E / N)}{P (N) P (E / N) + P (B) P (E / B)}$

Using Baye’s theorem, $P (N / E) = \frac{\frac{1}{4} \cdot \frac{1}{6}}{\frac{1}{4} \cdot \frac{1}{6} + \frac{3}{4} \cdot \frac{1}{3}} = \frac{1}{7}$

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