A team of workers including Tom and Dick work in the same office according to a schedule that ensures that exactly two team members will be present at a given time, and that in the course of the week all the team members work an equal number of hours. What is the probability that a visitor to the office who doesn’t know the schedule arrives to find both Tom and Dick in the office?
1) The team has three members.
2) Tom and Dick worked together for the whole of the previous day.
1. Assume a 3 day work week. Employees will be Tom (T), Dick (D) and Harry (H).
You don't need to work it out, but by combinations you have 3 possibilities
3! / ( 2! * (3-2)! ) = 6 / 2 * (1) = 6/2 = 3
Day 1 = TD
Day 2 = DH
Day 3 = TH
They all work the same amount, so the ratio of TD being in the office is 1:3.
2. So what, they worked yesterday. That doesn't matter