You own a company that employs three salespeople, Quentin, Michael and Bubba. Quentin makes 30% of the sales, Michael 45%, and Bubba 25%. While they are all competent, they do not enjoy completing the paperwork on their sales as required by the SEC. Of the sales Quentin makes, he completes paperwork 90% of the time. When Michael makes a sale, he completes the paperwork 80% of the time. When Bubba makes a sale, he completes paperwork 85% of the time. You were recently fined by the SEC for this reason, and have instituted tough new policies on this manner. However, you recently selected a file at random and found that the paper work was not in order. Who is the most likely culprit?

Michael

Step-by-step explanation:

Look at the table below:

The probability of selecting a sale that was made by Quentin is. 30, by Michael is. 45 and by Bubba is. 25.

Since Quentin completes paperwork 90% of the time, he doesn't complete paperwork 10% of the time, following this reasoning we can say that Michael doesn't complete paperwork 20% of the time and Bubba doesn't complete paperwork 15% of the time.

The probability of selecting a file and that it belongs to Quentin AND is incomplete is:

(Probability of selecting a Quentin's file) x (Probability is a Quentin incomplete file) = (0.30) (0.10) = 0.03

Using this same method we have that the probability that it belongs to Michael and is incomplete is (.45) (.20) = 0.09

That it belongs to Bubba and it's incomplete is (0.25) (0.15) = 0.037

The highest of these probabilities is the one that corresponds to Michael: 0.09, therefore he is the most likely culprit.