A team of workers including Tom and Dick work in the same office

Question

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) The team has three members.
(2) Tom and Dick worked together for the whole of the previous day.

VibhuAnurag · Answer

We need the probability that a random visitor finds both Tom and Dick in the office.
At any given time, exactly 2 team members are present.

Statement (1):  
 The team has 3 members. 
 Let the members be   Tom, Dick, and one other person.   Since exactly 2 people are present at any time, the possible pairs are: 
 Tom + Dick 
 Tom + Other 
 Dick + Other 
 Also, all team members work an equal number of hours.   That means these 3 pairs must occur for equal amounts of time. 
 So the probability that the visitor finds Tom and Dick together is   1/3. 
 Statement (1) is sufficient.

Statement (2):  
 Tom and Dick worked together for the whole of the previous day. 
 This tells us about one day only. It does not tell us   how many people are on the team,   how the rest of the schedule is arranged or   how often Tom and Dick work together during the week.   So we cannot determine the overall probability. 
 Statement (2) is not sufficient.

The answer is A.

Stella5200 · Answer

I thought of this as:

you are given there is a team and tom and dick are on it.

What isn the P(tom and dick).

pre solve: you need to know the number people on the team or some relationship

(1) give you # of members. this means the p of those two is (1/3) x (1/2) x (2! because there are 2 distinct people) = 1 x2/6 = 1/3.

Suff

(2) not relevant here

DAKSHGMAT · Answer

Okay, so this is how I worked it out

1. The team has three members

What I worked out from this was that the office has to choose exactly 2 members out of the three total. So we calculate the combinations of tom dick and the third worker; let's assume Harry.

Tom and dick
dick and Harry
Harry and Tom

Hence, there are a total of three combinations the office can choose from. Out of them, only one has Tom and dick working together. So the probability comes around to 1/3.

2. Tom and Dick worked together for the whole of the previous day.

This is, in my opinion, a distractor, as the question is about the probability of a random day, not this particular given day, so this is not adding anything and is insufficient.

Hence, for me, the first statement alone was sufficient and the answer was (A)

MrMaxMan · Answer

We have n people, two of which are T and D. We are picking 2 from them each day of the week.
The probability of picking T and D is the product of their two probabilities.
To know each probability you need to know the number of people you're picking from.
Statement 1 tells us how many people we have.  SUFF. 
Statement 2 tells us that they worked together on a specific day but that doesn't help us determine how many people we're picking from. It is irrelevant.  N.S.

A team of workers including Tom and Dick work in the same office

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A team of workers including Tom and Dick work in the same office

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