Question

A purse contains $2$ six-sided dice. One is a normal fair die,while the other has two $1^{\prime }s,$ two $3^{\prime }s$ and two $5^{\prime }$, A die is picked up and rolled. Because of some secret magnetic attration 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

• A. $1/7$
• B. $1/4$
• C. $1/6$
• D. $1/24$

Answer 1

The correct option is A $1/7$

Let N be the normal die picked, and M be the magnetic die picked and also let A be die shows up 3.

According to the question,

$P\left(N\right)=\frac{1}{4},P\left(M\right)=\frac{3}{4}$

$P\left(A\right)=P(A\cap N)+P(A\cap M)⟹P\left(A\right)=P\left(N\right)\times P\left(\frac{A}{N}\right)+P\left(M\right)\times P\left(\frac{A}{M}\right)⟹P\left(A\right)=\frac{1}{4}\times \frac{1}{6}+\frac{3}{4}\times \frac{1}{3}=\frac{1}{24}+\frac{1}{4}=\frac{7}{24}$

$P\left(\frac{N}{A}\right)=\frac{P(N\cap A)}{P\left(A\right)}=\frac{\frac{1}{4}\times \frac{1}{6}}{\frac{7}{24}}=\frac{1}{7}$

is the required probability.