Bayes Theorem Scenario

The Mamba plant uses two separate work shifts, day shift and night shift . The dayshift produces 65% of the product, while the night shift produces the remainder.

The Quality Control department said that 8% of the product from the morning shift is defective while 5%. of the night shift product is defective. The Bayes Theorem will help you determine the probability that these defects are an indicator of an underlying quality control issue. Construct a contingency table using the given probabilities and interpret your findings and suggest recommendations.Answer the following questions using the Bayes Theorem. In your response, make sure that you explain and justify your answers:

1. Given the finished product is defective, what is the probability it was produced during the day shift?(show work)

2. What is the probability the finished product was produced during the night shift given it is defective?(show work)

Princess Foods has the budget to provide one shift with additional training that should mitigate quality control issues. Should one shift undergo additional training?Use four decimal places. (show work)