Find the probability of no more than 2 successes in 5 trials of a binomial experiment in which the probability of success in any one trial is 18%.

P(x ≤ 2) = 0.96

Step-by-step explanation:

The formula is expressed as

P(x = r) = nCr × p^r × q^(n - r)

Where

x represent the number of successes.

p represents the probability of success.

q = (1 - r) represents the probability of failure.

n represents the number of trials or sample.

From the information given,

p = 18% = 18/100 = 0.18

q = 1 - p = 1 - 0.18

q = 0.82

n = 5

the probability of no more than 2 successes is expressed as P(x ≤ 2).

P(x ≤ 2) = P(x = 0) + P(x = 1) + P(x = 2)

Therefore,

P(x = 0) = 5C0 × 0.18^0 × 0.82^(5 - 0) = 0.37

P(x = 1) = 5C1 × 0.18^1 × 0.82^(5 - 1) = 0.41

P(x = 1) = 5C2 × 0.18^2 × 0.82^(5 - 2) = 0.18

P(x ≤ 2) = 0.37 + 0.41 + 0.18 = 0.96