Question

The probability that a part produced by a certain​ factory's assembly line will be defective is 0.022. Find the probabilities that in a run of 48 ​items, the following results are obtained.

​(a) Exactly 4 defective items

​(b) No defective items

​(c) At least 1 defective item

Answer 1

p = 0.022 and n = 48

P(X = r) = nCr * p^r * (1-p)^(n-r)

a)
P(X = 4) = 48C4 * 0.022^4 * (1-0.022)^44
= 0.0171

b)
P(X = 0) = 48C0 * 0.022^0 * (1-0.022)^48
= 0.3438

c)
P(X > = 1) = 1 - P(X = 0)
= 1 - 0.3438
= 0.6562