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A binomial experiment consists of four independent trials. the probability of success in each trial is 27?50 . find the probabilities of obtaining exactly 0 successes, 1 success, 2 successes, 3 successes, and 4 successes, respectively, in this experiment.

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nobillionaireNobley
The probability of a binomial distribution is given by
P(x) = nCx (p)^x (q)^(n - x)
where:
x is the number of successes.
n is the number of trials = 4.
p is the probability of success = 27/50 = 0.54.
q is the probability of failure = 1 - p = 1 - 0.54 = 0.46

P(0) = 4C0 (0.54)^0 (0.46)^4 = 1 x 1 x 0.0448 = 0.0448

P(1) = 4C1 (0.54)^1 (0.46)^3 = 4 x 0.54 x 0.0973 = 0.2102

P(2) = 4C2 (0.54)^2 (0.46)^2 = 6 x 0.2916 x 0.2116 = 0.3702

P(3) = 4C3 (0.54)^3 (0.46)^1 = 4 x 0.1575 x 0.46 = 0.2897

P(4) = 4C4 (0.54)^4 (0.46)^0 = 1 x 0.085 x 1 = 0.085.

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