A die is thrown two times and the sum
Question:

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

1. (1) $\frac{1}{4}$

2. (2) $\frac{1}{3}$

3. (3) $\frac{1}{8}$

4. (4) $\frac{1}{9}$

Correct Option: , 4

Solution:

$E_{1}$ [the event for getting score a multiple of 4 ]

$=(1,3),(3,1),(2,2),(2,6),(6,2),(3,5),(5,3),(4,4) \&(6,6)$

$E_{2}[4$ has appeared atleast once $]$

$=(1,4),(2,4),(3,4),(4,4),(5,4),(6,4),(4,1),(4,2),(4,3)$,

$(4,5) \&(4,6)$

$E_{1} \cap E_{2}=(4,4)$

$P\left(\frac{E_{2}}{E_{1}}\right)=\frac{1}{9}$