Q; In a manufacturing process it is estimated that 0.1% of the products are defective.

Question

1. In a manufacturing process it is estimated that 0.1% of the products are defective. If a client places an order for 25 of the products, what is the probability that at least two of them are defective?

Please provide a good, detailed explanation for this question, thank you.

Answer 1

There are various ways to do this. The formula based on a probability of one event happening and the only other possibility being that it doesn't happen for k ocurrences in a sample of size n:

P( k defects in a sample of size n) = _nC_k P^k (1-P)^n-k

Here k is 2, n is 25, P is .001. The C term is the combination of 25 things 2 at a time (which will equal 25*24/2)