Twenty tires are tested to see if they last as long as the manufacturer claims they do. Three tires fail the test. Two tires are selected at random without replacement for an inspection.

Question

Find the probability that both tires fail the test.
Which is greater, the probability that the first tire fails and the second one passes? or vice-versa?

Answer 1

p(f) = 3/20

p(first) = 3/20 = .15
p(second) = 2/19 = .105

p first and second = .15 * .105 = .0158

first fail, second pass
= 3/20 * 18/19

first pass second fail = 17/20 * 3/19