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

Explanation

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

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

`n(A)=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(B / A)=frac{n(A cap B)}{n(A)}=frac{2}{5}`