A purse contains 2 six-sided dice. One is normal fair die, while the other has two 1's, two 3's and two 5's. 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 a `25%` chance of picking a fair die. The die is rolled and shows up the face 3. The probability that a fair die was picked up is

Options

A. A. `1//7`
B. B. `1//4`
C. C. `1//6`
D. D. `1//24`

Answer

A

Explanation

Let N be the event of picking up a normal die, `P(N)=1//4` Let
M be the event of picking up a magnetic die, `P(M)=3//4.` Let
`P(A)=P(AnnN)+P(AnnM)`
`=P(N)P(A//N)+P(M)P(A//M)`
`=1/4xx1/6+3/4xx2/3=7/24`

`P(N//A)=(P(NnnA))/(P(A))`
`=((1//4)(1//6))/(7//24)=1/7`