Probability question

Question

A factory produces solar batteries. The probability of a new battery being defective is 3%. However, if the manager is on duty, the probability of a new battery being defective changes to 2%. The manager is on duty 39% of the time. Find the probability that the manager is on duty if a new battery is defective.

Answer is 29.9%

Thanks for your help.

Answer 1

P(D) = .03

P(D/M) = .02

P(M/D)= ? = .299?

P(M) = .39

this is a Bayes Theorem problem

P(M/D)P(D) = P(D/M)P(M) is Bayes Theorem

P(M/D) = P(D/M)P(M)/P(D) = .02(.39)/.03

= 2/3 of .39 = .26 not .29

Probability of the manager on duty given a defective = 0.26 = 26% not 29.9%