A die is rolled twice and the sum of the numbers appearing on them is observed to be 7. What is the conditional probability that the number 2 has appeared at least once?

Explanation

Total choices for numbers on the die for the total to be seven are as below:
`1+6,6+1,2+5,5+2,3+4,4+3`
Thus, there are 6 ways possible for the total to be seven.
so,here possible outcome is `=6`
Out of these six ways, there are `2 ways` where `2` is one of the outcome.
so,here desired outcome`=2`
Hence the probability of occurrence of 2 becomes
=(desired outcome)/(possible outcome)
`=2/6`
`=1/3`