Let’s put some other words into the secretary’s dialogue. What if she had said the following?Secretary: When employees choose to take off a pair of sick days in a Tuesday–Monday period of time, 40% of the time they choose Friday and Monday as the two days they pick!The following two questions explore in what sense this is or is not a different situation than the one in the actual cartoon.Question: If we denote the five usual workdays as M,T,W,R, and F (using R for Thursday), which of the following lists all pairs of possible workdays.Group of answer choices(M,F), (T,F), (T,M), (W,M), (W,F), (R,M), (R,F), (F,W), (F,R), (M,R)(M,T), (M,W), (M,R), (M,F), (T,W), (R,M), (T, F), (R,W), (W,F), (R,F)(M,T), (T,W), (W,R), (R,F), (T,M), (W,T), (R,W), (F,R), (M,F), (F,T)iii. (M,T), (M,W), (M,R), (M,F), (T,W), (T,R), (T, F), (W,R), (W,F), (R,F)
Question
Let’s put some other words into the secretary’s dialogue. What if she had said the following?Secretary: When employees choose to take off a pair of sick days in a Tuesday–Monday period of time, 40% of the time they choose Friday and Monday as the two days they pick!The following two questions explore in what sense this is or is not a different situation than the one in the actual cartoon.Question: If we denote the five usual workdays as M,T,W,R, and F (using R for Thursday), which of the following lists all pairs of possible workdays.Group of answer choices(M,F), (T,F), (T,M), (W,M), (W,F), (R,M), (R,F), (F,W), (F,R), (M,R)(M,T), (M,W), (M,R), (M,F), (T,W), (R,M), (T, F), (R,W), (W,F), (R,F)(M,T), (T,W), (W,R), (R,F), (T,M), (W,T), (R,W), (F,R), (M,F), (F,T)iii. (M,T), (M,W), (M,R), (M,F), (T,W), (T,R), (T, F), (W,R), (W,F), (R,F)
Solution
The correct answer is (M,T), (M,W), (M,R), (M,F), (T,W), (T,R), (T, F), (W,R), (W,F), (R,F).
Here's why:
We are looking for all possible pairs of workdays. The pairs should not repeat, meaning (M,T) is the same as (T,M), so we only count it once.
Starting with Monday (M), we can pair it with Tuesday (T), Wednesday (W), Thursday (R), and Friday (F).
Next, starting with Tuesday (T), we can pair it with Wednesday (W), Thursday (R), and Friday (F). We don't pair it with Monday because we already counted that pair when we started with Monday.
We follow the same pattern for the remaining days. Starting with Wednesday (W), we pair it with Thursday (R) and Friday (F).
Finally, starting with Thursday (R), we pair it with Friday (F).
So, the pairs are (M,T), (M,W), (M,R), (M,F), (T,W), (T,R), (T, F), (W,R), (W,F), (R,F).
Similar Questions
Difficult Dilbert DialogueThe following dialogue is from a Dilbert cartoon published April 17, 1996.Secretary: Oh my! This is shocking!Boss: What?Secretary: 40% of all sick days taken by our staff are Fridays and Mondays!Boss: What kind of idiot do they think I am?Secretary: Not an idiot savant, they can do math.The secretary is trying to poke fun at her pointy-headed boss. Is she successful or is the joke on her?Group of answer choicesJoke’s on her. Assuming an employee picks a single workday at random to be absent, the chances that the employee will pick a Monday or a Friday are 2 in 3, not 2 in 5, since once two days are counted, you only have three left.Joke's on her. Assuming an employee picks a single workday at random to be absent, the chances that the employee will pick a Monday or a Friday are 2/5 which is 2.5%, so the author of the cartoon was having his own numeracy issues.i. Successful. Assuming an employee picks a single workday at random to be absent, the chances that the employee will pick a Monday or a Friday are 2/5 which is 40%Successful. Assuming an employee picks a single workday at random to be absent, the chances that the employee will pick a Monday or a Friday are (1/2) × (1/2)—since there is a 1 in 2 chance they pick a Monday or they don’t—which is 1/4, or about 40%
Assume there are ten possible pairs of days an employee could pick from, and that list of the sets of ten pairs suggested in the question above is the right one. If a pair was just picked at random, what is the chance that they’d pick Monday and Friday as the pair, and does this suggest the secretary (in the amended dialogue) has uncovered a bias?Group of answer choices1 in 10. No evidence of bias since every pair had an equal chance of being chosen.1 in 10. Yes, if 40% are choosing Monday and Friday, that is evidence of bias toward that pair.4 in 10. But that is the exactly what the secretary notices was happening, so no evidence of bias.4 in 10. Yes, if 40% are choosing that pair of days, and there is exactly that chance of randomly choosing that pair of days, then this is clear evidence of bias in the days the employees are choosing.
In a four-day period Monday through Thursday each of the following temporary office workers worked only one day, each a different day. Ms. Johnson was scheduled to work on Monday, but she traded with Mr. Carter, who was originally scheduled to work on Wednesday. Ms. Falk traded with Mr. Kirk, who was originally scheduled to work on Thursday. On what day, Ms. Falk was originally scheduled to work?*1 pointThursdayTuesdayMondayWednesday
Do not schedule more than __________ interview(s) on the same day.Group of answer choicesonefourtwothree
3. What day follows the day before yesterday if two days from now will be Sunday?MondayTuesdayWednesdayThursdayFridaySaturdaySunday
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