Q4 An automobile transmission can fail due to three types of

Q4. An automobile transmission can fail due to three types of problems i.e. gear failure, bearing failure, or shaft failure, wit probabilities 0.3 0.5 an 0.2 respectively. The probability of transmission failure given a gear failure is 0.5, given a bearing failure is 0.5 and given a shaft failure is 0.6. If a transmission fails, what is the most likely cause?

Solution

Failures              Gear               Bearing                Shaft

prob                    0.3                    0.5                      0.2

Transm fail          0.5                    0.5                      0.6

comp prob          0.15                   0.25                     0.12

As the composite prob is more for Bearing, the most likely cause is the defect in the bearing