Mathematics

The key insight is that empirical probability is just the ratio of successes to total attempts—so you need to find how many more successes will push that fraction to at least $0.5$. Set up an inequality where the numerator is her current successes plus $n$ new ones, and the denominator is her current total plus $n$ attempts, then solve for the smallest integer $n$ that makes the ratio at least $\frac{1}{2}$.

The key insight is that empirical probability is just the ratio of successes to total attempts—so you need to find how many more successes will push that fraction to at least $0.5$. Set up an inequality where the numerator is her current successes plus $n$ new ones, and the denominator is her current total plus $n$ attempts, then solve for the smallest integer $n$ that makes the ratio at least $\frac{1}{2}$.