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what is the mean of this binomial probability distribution?

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Hi Sheily,
For this case, we have that p = 0.25 and n = 15. Then, we can model this distribution as B(15,0.25). The expected value, otherwise known as the mean, is given as follows:
E(X) = np
        = 15(0.25)
        = 3.75
Interpreting this result, we can expect to win approximately 4 out of the 15 hands.