I am reading through a book teaching Binomial Probability. Using the Binomial Distribution Formula , they define ‘$n$’ as being $n$ independent trials of the same experiment. Which makes sense. Rolling the same dice $6$ times is $n = 6$. However I got confused when the book presented me with this problem: “six dice are rolled. Find the probability that two of them show a four” answer is $0.200939$, but only if one considers rolling $6$ dice at the same time as $6$ trials of the same experiment. In my mind throwing six dice at the same time is a specific experiment done only one time, thus $n = 1$. Maybe I am misinterpreting the question. What am I missing in my understanding?
2026-03-29 19:09:43.1774811383
What exactly is considered ‘$n$’ experiments in Binomial Probability?
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The Binomial distribution is defined as the number of successes in $n$ independent Bernoulli trials (experiments). So $n$ is number of Bernoulli trials. Nothing is assumed about organizing Bernoulli trials, they need to be independent and have fixed probability of success only.