Question

A die is thrown twice and the sum of the numbers appearing is observed to be 6. What is the probability that the number 4 has appeared at least once?

Answer 1

$A=$ sum of the numbers appearing on two dice is 6

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

$n\left(A\right)=5$

$B=$ number 4 has appeared at least once

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

$A\cap B=(2,4),(4,2)$

$n(A\cap B)=2$

Required probability = $P\left(B/A\right)=\frac{n(A\cap B)}{n\left(A\right)}=\frac{2}{5}$