A dice 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= dice shows `4`

B=shows sum of numbers on two dice is `6` .

`A={(1,4)(2,4),(3,4),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,4),(6,4)} `

`
B={(1,5),(5,1),(2,4),(4,2),(3,3)}`



Then ,

`
A cap B={(2,4) and (4,2)}`

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