Question

A dice is thrown two times and the sum of the scores appearing on the dice is observed to be a multiple of $4$. Then the conditional probability that the score $4$ has appeared atleast once is

• A. $\frac{1}{3}$
• B. $\frac{1}{4}$
• C. $\frac{1}{8}$
• D. $\frac{1}{9}$

Answer 1

The correct option is D $\frac{1}{9}$

$A:$ Sum obtained is a multiple of $4.$
$A=\left\{\right(1,3),(3,1),(2,6),(6,2),(3,5),(5,3),(2,2),(4,4),(6,6\left)\right\}$

$B:$ Score of $4$ has appeared at least once.
​​$B=\left\{\right(1,4),(2,4),(3,4),(4,4),(5,4),(6,4),(4,1),(4,2),(4,3),(4,5),(4,6\left)\right\}$

From $A$ and $B,$
$(A\cap B)=(4,4),n(A\cap B)=1$

Required probability $=P\left(\frac{B}{A}\right)=\frac{P(A\cap B)}{P\left(A\right)}=\frac{\frac{1}{36}}{\frac{9}{36}}=\frac{1}{9}$