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Binomial Distribution

In a lab experiment involving inorganic syntheses of molecular precursors to organometallic ceramics, the final step of a five-step reaction involves the formation of a metal-metal bond. The probability of such a bond forming is p = 0.20. Let X equal the number of successful reactions out of n = 25 such experiments.
a) Find the probability that X is at most 4
b) Find the probability that X is at least 5
c) Find the probability that X is equal to 6
d) Give the mean, variance, and standard deviation of X

An urn contains 7 red and 11 white balls. Draw one ball at random from the urn. Let X =1 if a red ball is drawn, and let X =0 if a white ball is drawn. Give the p.m.f., mean and variance of X.

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The solution contains the determination of p.m.f., mean and variance of a Binomial distribution for several problems.

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