A deck contains cards numbered $$1,2,\ldots,52$$. After $$13$$ random cards are discarded, one card is chosen randomly from the remaining $$39$$ cards. If the probability that its number is a multiple of $$13$$ is $$\frac{m}{n}$$ in lowest terms, then $$m+n$$ is
Correct Answer: 14
Solution
The final selected card is equally likely to be any one of the original $$52$$ cards because the discard and selection process is symmetric. There are $$4$$ multiples of $$13$$ among these cards. Hence the probability is $$\frac{4}{52}=\frac{1}{13}$$, so $$m+n=14$$.
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