Question

A local company that provides home repair services
for appliances has two repairmen who make all of
the home repairs. The company sends Repairman D
on 70% of all jobs because the likelihood of him getting
a second follow-up call within a week is only
0.08, whereas the probability of Repairman K getting
a second follow-up call within a week is 0.20.
If you recently had a repair job done at your home
and it requires a second follow-up call, what is the
probability that Repairman K did your initial repair
work?

Answer 1

Given,

P(D) = 0.70

So P(K) = 1 - 0.70 = 0.30

P(Second follow up | D) = 0.08

P(Second follow up | K) = 0.20

Hence by Baye's theorem:

P(K | Second follow up)

0.20 0.30 0.70 0.08 0.20 0.30

= 0.5172