Four pharmacists at a drugstore were observed over three days to evaluate their performance. Data was collected on the percentage of prescriptions filled and receipts forgotten for each pharmacist. Given that a customer received a prescription without a receipt, there is a 37.7% probability it was prepared by Shirley, who had the highest percentage of receipts forgotten at 10%.

1. Four employees who work as pharmacists at a drugstore are being evaluated. As part of quality
improvement initiative and employee evaluation these workers were observed over three days.
One of the statistics collected is the proportion of time a pharmacists forgot to include a receipt
in the bag. Related information is given in the table.
worker % of prescriptions filled % of receipts forgotten
dan 25% 6%
steve 20% 2%
shirley 20% 10%
tom 35% 4%
You just picked up a prescription and found that there is no receipt in your bag, what is the
probability that shirley has prepared your order?
Solution
P(prepared by Cheryl | napkin forgotten) = [20% * 10%] / [25% * 6% + 20% * 2%
+ 20% * 10% + 35% * 4%] = 200 / [150 + 40 + 200 + 140] = 200 / 530 = 20 / 53 = 0.37735849
= 37.7%