Thus, the probability that exactly two of the four rolls result in a number greater than 7 is:

February 22, 2026

Thus, the probability that exactly two of the four rolls result in a number greater than 7 is:

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P(k) = \binom{n}{k} p^k (1 - p)^{n - k}
Substitute the values:
P(2) = \binom{4}{2} (0.3)^2 (0.7)^2 = 6 \cdot (0.09) \cdot (0.49) = 6 \cdot 0.0441 = 0.2646
\boxed{0.2646}
Question: A science administrator is reviewing grant applications and notices that each letter of a 7-character activity code is either 'E', 'X', or 'Y'. How many such codes contain exactly three 'E's and at least one pair of consecutive identical letters?
We are to count the number of 7-character strings using only the letters 'E', 'X', 'Y' such that:

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