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.

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.