Question

A sample of 20 different iPads is randomly selected from a production batch containing 3% defectives.

What is the probability that exactly 4 are working properly?

What is the probability that at most one from the 20 randomly selected is defective?

Answer 1

X ~ Bin ( n , p)

Binomial probability distribution is

P(X) = nCx * px * ( 1 - p)n-x

a)

n = 20 , p = 1 -0.03 = 0.97

P(X = 4) = 20C4 * 0.974 * ( 1 - 0.97)16

= 0.0000

b)

n = 20 , p = 0.03

P(X <= 1 ) = P(X = 0) + P(X = 1)

= 20C0 * 0.030 * ( 1 - 0.03)20 + 20C1 * 0.031 * ( 1 - 0.03)19

= 0.8802