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A twenty-sided die, with the faces numbered 1 to 20, is rolled 100 times. What is the exact probability of getting more than 15 elevens but at most 30 elevens?

Answer :

Final answer:

To find the exact probability of getting more than 15 but at most 30 elevens when rolling a twenty-sided die 100 times, we can use the binomial probability formula and calculate each individual probability.

Explanation:

To find the probability of getting more than 15 elevens but at most 30 elevens when rolling a twenty-sided die 100 times, we need to calculate the probability of getting exactly 16, 17, 18, ..., 30 elevens and add them together. To calculate the probability of getting exactly k elevens, we can use the binomial probability formula:

P(X = k) = (100 choose k) * (1/20)^k * (19/20)^(100-k)

We can then calculate each individual probability and sum them up to get the exact probability.

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