Question

A contractor purchases a shipment of 100 transistors. It is his policy to test 10 of these transistors and to keep the shipment only if at least 9 out of the 10 are in working condition. If the shipment contains 20 defective transistors, what is the probability it will be kept?

Please clearly label and explain all steps and all functions used. I am looking to understand not just get the answer.

Answer 1

This is a hypergeometric distribution. We have 20 defective transistors and  80 good transistors in the shipment.

We can use combinations to compute the following probability

Pr[9 or 10 Good] = Pr[9 Good] + Pr[10 Good]

P[X9]
= P[9]+P[10]
= (10C9)(0.8)^9 *(0.2)^(10-9) + (10 C10)(0.8)^10 * (0.2)^0
= 10*0.8^9 *0.2 + 0.8^10
= 0.26842 + 0.107374
= 0.37577