Wirless sets are manufactured with 25 soldered joints each on the average 1 joint in 500 is defective.

Question

How many sets can be expected to be free from defective joints in a consignment of 10000 sets?

Answer 1

Let's start with one wireless set. In order to be defect free, every 25 joints must be perfect. The probability that a single joint is defective is 1/500, so the probability that it's NOT defective is 499/500. We can probably assume that the defect of a solder is independent so that in order for all 25 solders to be perfect, we compute (499/500)^25 = 0.95118

 

So that's the probability that one wireless set is defect free. What we want is the expected value of 10000X where X is a single defect-free wireless set.

 

E(10000X) = 10000E(X)    - this is true because expectations are linear functions

E(X) = 0.95118 - this is the probability that a single unit is defect free.

 

So we would exect 0.95118 * 10000 to be defect free, which equals 9511.81