Answer: 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
