The Cobot has a health monitoring system to provide information regarding the status of critical subsystems. Automated health checks of the position encoder are conducted at regularly timed intervals (200 ms). Based on testing performed, the health check of the position encoder is said to be 95% accurate (e.g., if the health check reports an encoder failure, then there is a 95% chance the encoder is actually failed). The first prototype Cobot is under operational testing and test engineers just reported that the Cobot reported a failed health check of the encoder. Examination of encoder reliability data, based on previous experience in other systems) shows that the probability of the part failure at its current age is only 0.015.

a. Use Bayesian logic to calculate the probability that the encoder is actually failed, given the automated health check reported an encoder failure.

b. What is the probability that the position encoder is not actually failed.