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

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Math Expert
Joined: 02 Sep 2009
Posts: 60779
A team of workers including Tom and Dick work in the same office accor  [#permalink]

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22 May 2016, 13:33
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25% (medium)

Question Stats:

71% (01:32) correct 29% (01:53) wrong based on 170 sessions

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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.

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Re: A team of workers including Tom and Dick work in the same office accor  [#permalink]

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22 May 2016, 20:50
Bunuel wrote:
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.

Tom and Dick have the same probability as any other two of the team have..
so we basically require to know overall number..

(1) The team has three members.
since team has 3 members, ways to select 2 out of 3 = 3C2 = 3ways..
Out of these 3 ways, ONLY one will contain T and D, so P = 1/3
Suff

(2) Tom and Dick worked together for the whole of the previous day.
we do not know about how many OTHER groups can be there..
Insuff

A
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Re: A team of workers including Tom and Dick work in the same office accor  [#permalink]

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04 Aug 2016, 06:20
1
Bunuel wrote:
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.
So based on the stimulus there has to be two members present in the office
Possiblities are :-{Tom & Dick} {Tom & Unnamed Member} {Dick & Unnamed member} ; Total 3 possibilities ; Favorable = 1 {Tom & Dick }; Probablity = 1/3

(2) Tom and Dick worked together for the whole of the previous day.
First we do not know how many work days are in the thier companies week. Is it monday to saturday or Monday to Friday
We do not what time table the company follows.
MONDAY= TOM AND DICK----->THIRD ONE ON HOLIDAY
TUESDAY=TOM AND DICK ----------> THIRD ONE ON HOLIDAY
WEDNESDAY=TOM AND THIRD ----> DICK ON HOLIDAY
THURSDAY=DICK AND THIRD-----> TOM ON HOLIDAY
FRIDAY= DICK AND THIRD -----> TOM ON HOLIDAY
SATURDAY =TOM AND THIRD ---> DICK ON HOLIDAY
SUNDAY= ALL THREE WORK
ALL WORK 5 DAYS AND ALL TAKE 2 DAYS LEAVE
Now we dont know when the stranger will come to visit.
If he comes on Tuesday, he has 100% probability of finding both tom and dick
If he comes on Wednesday, he has 0% probablity of finding both tom and dick

INSUFFICIENT

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Re: A team of workers including Tom and Dick work in the same office accor  [#permalink]

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10 Dec 2019, 22:09
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Re: A team of workers including Tom and Dick work in the same office accor   [#permalink] 10 Dec 2019, 22:09
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# A team of workers including Tom and Dick work in the same office accor

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