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We have a question to investigate any game between two players that have dice, when the dice are rolled $4$ times what is the probability of getting any number say $4$ or $5$.. note that the highest number is taken. So if a player gets $1,1,1,4$ or $1,2,5,3$ the highest number is taken to go against the other player. So what is the probability of getting the highest number as $1$ which is $1/1296$ and $2$ is $15/1296$, 3 is $56/1296$ but I can't seem to figure out a pattern or to create an equation to get the rest of the probability.

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Do you mean that only one of the highest number is taken? what about 1,1,5,5,5. Would then the three 5's be taken? Also, have you considered 1,1,1,1,1? – yiyi Oct 30 '12 at 11:52

Hint: Let $N$ denote that number. Surely one can compute $\mathbb P(N\leqslant n)$ for each $1\leqslant n\leqslant6$, right? Then, $\mathbb P(N=n)=\mathbb P(N\leqslant n)-\mathbb P(N\leqslant n-1)$.

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