A die is thrown twice and the sum of the numbers appearing is observed to be 7. Find the conditional probability that the number 3 has appeared at least once.
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Solution
Total options for numbers on the die for the sum to be 7 are as below:
1+6,6+1,2+5,5+2,3+4,4+3
Thus, there are 6 ways possible for the sum to be 7.
Out of these six ways, there are 2 ways where 3 is one of the outcome and so the probability of occurrence of 3 becomes 36=12