Question

A quality control engineer tests the quality of produced computers in a shipment of 6 computers. Suppose that 5% of computers have defects, and defects occur independently of each other.

(a) Find the probability of exactly 2 defective computers in the shipment.

(b) Find the probability of at most 2 defective computers in the shipment.

Answer 1

a)

Here, n = 6, p = 0.05, (1 - p) = 0.95 and x = 2
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X = 2)
P(X = 2) = 6C2 * 0.05^2 * 0.95^4
P(X = 2) = 0.0305

b)

Here, n = 6, p = 0.05, (1 - p) = 0.95 and x = 2
As per binomial distribution formula P(X = x) = nCx * p^x * (1 - p)^(n - x)

We need to calculate P(X <= 2).
P(X <= 2) = (6C0 * 0.05^0 * 0.95^6) + (6C1 * 0.05^1 * 0.95^5) + (6C2 * 0.05^2 * 0.95^4)
P(X <= 2) = 0.7351 + 0.2321 + 0.0305
P(X <= 2) = 0.9977