Probability

Question

A box of parts has 8 working parts and 5 defective parts. What is the probability that if 2 parts are selected at random, at least one part is defective?

Answer 1

P(at least 1/2 parts are defective) = 1 - P(none are defective)

 

We can solve using the hypergeometric distribution formula.  This is essentially saying the number of ways you can pull 2 working parts from the sample of 8 working parts times the number of ways to pull 0 defective parts from the sample of 5 defective parts, divided by all of the ways you can pull any 2 parts from the total population of 13 parts (defective or working).

 

(8C2 * 5C0)/(13C2)

= 28/78

=.359

 

So the P(at least 1 is defective) = 1 - .359 = .641.