Question: A company manufactures thousands of wigets each day. On a good day, only 0.6% of the production is defective. However, bad days occur 15% of the time, and 11% of the production is defective on these days.

A sample of five wigets is chosen at random from the days production. Each wiget in the sample is inspected to determine if it is defective or not defective. The number of defective wigets found will be between 0 and 5.

Using a spreadsheet, answer the following questions:

a) What are the probabilities of finding 0-5 (inclusive) defective wigets in the sample for each type of day?

b) What are the posterior probabilities of a "good day" and "bad day" conditional on the number of defective wigets?