Question

You would like to evaluate the probability of success for testing a batch of n processors. To start out, let’s assume that if there is a problem with the batch, exactly 1 out of the n processors are defective. You are willing to test only k of the processors (due to budget or times constraints).

(a) How many ways are there of testing k out of n processors?

(b) How many ways are there of testing k processors with the defective processor included?

(c) Use your answers from parts (a) and (b) to determine the probability of catching a defective batch.

(d) Evaluate your answer from part (c) for n = 20 and k = 5.

(e) Now, say that a defective batch contains exactly 3 defective processors. How many ways are there of testing k processors with at least one defective processor included? (You may assume that k > 3.)

(f) Use your answer from part (e) to determine the probability of catching a defective batch.

(g) Evaluate your answer from part (f) for n = 20 and k = 5.

Answer 1

(a) Number of ways of testing out k out of n processors =

(b) Number of ways of testing k processors with the defective processor included =

(c) The probability of catching a defective batch = = k/n

(d) The required probability = 5/20 = 0.25

(e) The required probability = Total Number of ways of testing out k out of n processors - Number of ways of testing out k out of n processors with no defective processor included

=

(f) The required probability =

(g) For n = 20, k = 5, the probability = 0.601