4. Two technicians regularly make repairs when breakdowns occur on an automated production line. The first technician, who services 40% of the breakdowns, has 5% chance of making incomplete repair. The second technician, who services 60% of the breakdowns, has a 3% chance of making an incomplete repair. Given that there is a problem with the production line due to an incomplete repair, what is the probability that this initial repair was made by the first technician

52.63% probability that this initial repair was made by the first technician

Step-by-step explanation:

Bayes Theorem:

Two events, A and B.

In which P(B|A) is the probability of B happening when A has happened and P(A|B) is the probability of A happening when B has happened.

In this question:

Event A: Error due to an incomplete repair.

Event B: Initial repair made by the first technican.

The first technician, who services 40% of the breakdowns, has 5% chance of making incomplete repair.

This means that

Probability of an incomplete repair:

5% of 40%(first technican)

3% of 60%(second technican).

Then

Given that there is a problem with the production line due to an incomplete repair, what is the probability that this initial repair was made by the first technician

52.63% probability that this initial repair was made by the first technician