The local diner employs three servers, Ally, Benny, and Charli. On Monday night Ally served 40% of the customers, while Benny served 27%. What percent did Charli serve?

Question

a. The local diner employs three servers, Ally, Benny, and Charli. On Monday night Ally served 40% of the customers, while Benny served 27%. What percent did Charli serve?

b. That night 60% of Ally's customers ordered pie, while 40% did not. Of Benny's customers, 20% ordered pie. What percent did not?

c. Find the probability that a customer ordered pie on Monday night.

d. Given that a customer ordered pie that night, what is the probability that their server was Ally? Round to the nearest whole percent.

LINK TO THE CHART: https://docs.google.com/document/d/19YmNm_F0QQjNLbhAs2Qzr8wI_hYZ78bdjp4IfPymoHo/edit?usp=sharing

Answer 1

a) charlie served 100-40-27 = 100-67= 33% of the customers

b) 20% of Benny's customers ordered pie. 100-20 = 80% of Benny's customers did not order pie.

c) .4 x 40% + .8 x 27% = 16% + 21.6%. a lower bound is 38.2%, if all of Charlie's customers ordered pie. An upper bound is if all Charlie's customers did not order pie, of 33% + 38.2% = 71.2%

The percentage who did not order pie = N, with 38.2% < N < 71.2%

d) if a customer ordered pie, what is the probability Ally served them? 60% of Ally's customers ordered pie. 20% of Benny's ordered pie. If 100% of Charlie's ordered pie, then .6(40%) = 24% of the customers were Ally customers who ordered pie, and .2(27%) + (33%) + 24% = 5.4+33+24 = 62.4% of all customers ordered pie. Odds a customer who ordered pie was Ally's is 24/62.4 = about 38% rounded off to nearest integer as a lower bound. But if none of Charlie's customers ordered pie then the percent of customers who ordered pie = 24+5.4= 29.4% and 24/29.4 = 82% chance that customer was Abby's customer

38% < A < 82% = odds a customer who ordered pie was Abby's

There's more information, particularly what percent of Charlie's customers ordered pie. If that were known you could get a unique solution rather than just a range of possible solutions. It may be in another website, but it's not given explicitly in this problem. without that information, maybe best estimate is the middle percentage in the ranges above