Question

Three technicians make repairs when breakdown occur on an automated production line. Ramy who services 20% of the breakdown, makes an incomplete repair 1 time in 20, Jenifer who services 15% of the breakdown, makes an incomplete repair 1 time in 10, Huzaifa who services 5% of the breakdown makes an incomplete repair 1 time in 20. For the next problem when an initial repair that was incomplete, what is the probability that initial repair was done by Ramy?

Answer 1

Answer:

Given,

To determine the probability that initial repair was done by Ramy

let us consider the bayes theorem of conditional probability

P(Ramy | incomplete repair) = ?

consider,

P(Incomplete repair) = P(repairer)*P(work left incomplete by him)

= 0.20*1/20 + 0.15*1/10 + 0.05*1/20

= 0.01+0.015+0.0025

P(Incomplete repair) = 0.0275

P(Incomplete repair) = 0.0275

Now P(Ramy | incomplete repair) = (0.20 * (1/20) ) / 0.0275

= 0.01/0.0275

= 0.3636

Required probability = 0.3636