Assume that a procedure yields a binomial distribution with a trial repeated n times. Use the binomial probability formula to find the probability of x successes given the probability p of success on a single trial. Round to three decimal places.
n = 64, x = 3, p = 0.04
(1 point)
The binomial probability formula is given by:
P(X = x) = (nCx) * p^x * (1-p)^(n-x)
where:
n = number of trials
x = number of successes
p = probability of success on a single trial
Using the given values:
n = 64
x = 3
p = 0.04
P(X = 3) = (64C3) * (0.04)^3 * (1-0.04)^(64-3)
Calculating each term:
64C3 = (64!)/(3!(64-3)!) = 41664
(0.04)^3 = 0.000064
(1-0.04)^(64-3) = 0.961
P(X = 3) = 41664 * 0.000064 * 0.961
P(X = 3) ≈ 2.528
Therefore, the probability of getting exactly 3 successes out of 64 trials, with a success probability of 0.04 on a single trial, is approximately 0.003.