Question

machine produces an average of 20% defective bolts. A batch is accepted if a sample of 5 bolts taken from that batch contains no defective and rejected it the sample contains 3 or more defectives. In other cases, a second sample is taken. What is the probability that the second sample is required ?

Answer 1

machine produces an average of 20% defective bolts. A batch is accepted if a sample of 5 bolts taken from that batch contains no defective and rejected it the sample contains 3 or more defectives. In other cases, a second sample is taken. What is the probability that the second sample is required ?

Answer 2

The other case (when a second sample is required) is when there is 1 or 2 out of 5 that are defective.

p(1) = 5C1*(0.2^1)*(0.8^4) = 5*(0.2^1)*(0.8^4) = 0.4096

p(2) = 5C2*(0.2^2)*(0.8^3) = 10*(0.2^2)*(0.8^3) = 0.2048

Probability that a second sample is required = p(1) + p(2) = 0.6144