harsh.champ wrote:A team of workers including Rob and Martin 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 Rob and Martin in the office?

1. The team has three members.
2. Rob and Martin worked together for the whole of the previous day.

Thats a great probability question!

Right off the bat I think of the definition of probability:

Total number of "successful" outcomes / Total number of outcomes

So we can obviously see that (2) is not sufficient because it doesn't give us any information about the total number of outcomes. What we need is information about the total number of outcomes.

(1) gives us this. It tells you that you have 3 team members. Thus there are the following work events, with the mystery third member denoted as X

E1 = R,M
E2 = R,X
E3 = M,X

Thus there are 3 total events and 1 successful event. Since the problem states that all employees work equally, each event is weighted equally with a probability of 1/3. Hence (1) gives us (1/3) and the answer is (a).

I think where this problem becomes tricky is, in looking at (1) you say "oh yeah, that's enough information" but then in looking at (2) you think "oh crap I need to know who has already worked what this week" The definition of (d) is "(1) and (2) individually are not sufficient, but together they are sufficient" Actually (1) and (2) together are sufficient and you will come up with a different answer than just with (1) alone, but that is not what the question is asking.

1) Total no of people is 3 . So 3C2 = 6 is the number of possibilities. Kind of forcing us to assume it is a 6 day week. Probability of finding R and M together is 2/6. Sufficient.
2) If they worked together yesterday they will work once more so the probability is 1/5. But this info does not helps us to find the probability but states a condition. Not necessary.
IMO A