Question

# A dice 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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Hint: Count the number of cases such that the sum of the number is 7 and find the probability of occurrence of 3 out of those cases.

So, the conditional probability = $\dfrac{{{\text{no}}{\text{. of cases when the numbered 3 occured at least once}}}}{{{\text{total number of cases when the sum is 7}}}}$
=$\dfrac{2}{6}$
=$\dfrac{1}{3}$
Hence, the required answer is $\dfrac{1}{3}$.