<p>A pair of fair <img alt="$6$" height="12" src="https://latex.artofproblemsolving.com/6/0/1/601a7806cbfad68196c43a4665871f8c3186802e.png" width="8" />-sided dice is rolled <img alt="$n$" height="8" src="https://latex.artofproblemsolving.com/1/7/4/174fadd07fd54c9afe288e96558c92e0c1da733a.png" width="10" /> times. What is the least value of <img alt="$n$" height="8" src="https://latex.artofproblemsolving.com/1/7/4/174fadd07fd54c9afe288e96558c92e0c1da733a.png" width="10" /> such that the probability that the sum of the numbers face up on a roll equals <img alt="$7$" height="12" src="https://latex.artofproblemsolving.com/e/0/a/e0a0db32027a732ac57d37ef2ae9bb150f65b108.png" width="9" /> at least once is greater than <img alt="$\frac{1}{2}$" height="37" src="https://latex.artofproblemsolving.com/2/f/9/2f960094315d60883495f9b74148e17487ee9584.png" width="11" />?</p>

Question No: 353

A pair of fair $6$ -sided dice is rolled $n$ times. What is the least value of $n$ such that the probability that the sum of the numbers face up on a roll equals $7$ at least once is greater than $\frac{1}{2}$ ?

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Tags: Combinatorics Probability

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