Maximize Probability on a Weighted Coin

Discrete Mathematics Level 3

Daniel has a weighted coin that flips heads $\frac{2}{5}$ of the time and tails $\frac{3}{5}$ of the time. If he flips it $9$ times, the probability that it will show heads exactly $n$ times is greater than or equal to the probability that it will show heads exactly $k$ times, for all $k=0, 1,\dots, 9, k\ne n$ .

If the probability that the coin will show heads exactly $n$ times in $9$ flips is $\frac{p}{q}$ for positive coprime integers $p$ and $q$ , then find the last three digits of $p$ .

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Maximize Probability on a Weighted Coin

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 7 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.

Learn from a vibrant community of students and enthusiasts,
including olympiad champions, researchers, and professionals.