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# Jack and Jill work at a hospital with 4 other workers. For a

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Jack and Jill work at a hospital with 4 other workers. For a  [#permalink]

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Updated on: 14 Jun 2013, 10:29
1
5
00:00

Difficulty:

25% (medium)

Question Stats:

74% (01:23) correct 26% (01:30) wrong based on 198 sessions

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Jack and Jill work at a hospital with 4 other workers. For an internal review, 2 of the 6 workers will be randomly chosen to be interviewed. What is the probability that Jack and Jill will both be chosen?

(A) 1/3
(B) 1/4
(C) 1/15
(D) 3/8
(E) 2/3

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Originally posted by atalpanditgmat on 14 Jun 2013, 10:19.
Last edited by Bunuel on 14 Jun 2013, 10:29, edited 2 times in total.
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Re: Jack and Jill work at a hospital with 4 other workers. For a  [#permalink]

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14 Jun 2013, 14:50
3
2
Total number of people = 6

Probability of selecting Jack first and then Jill is $$\frac{1}{6}$$$$*\frac{1}{5}$$$$=\frac{1}{30}$$
Probability of selecting Jill first and then Jack is $$\frac{1}{6}$$$$*\frac{1}{5}$$$$=\frac{1}{30}$$

Therefore probability of selecting Jack and Jill for the review is $$\frac{1}{30}$$$$+\frac{1}{30}$$$$=\frac{1}{15}$$

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Posts: 51101
Re: Jack and Jill work at a hospital with 4 other workers. For a  [#permalink]

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14 Jun 2013, 10:30
2
atalpanditgmat wrote:
Jack and Jill work at a hospital with 4 other workers. For an internal review, 2 of the 6 workers will be randomly chosen to be interviewed. What is the probability that Jack and Jill will both be chosen?

(A) 1/3
(B) 1/4
(C) 1/15
(D) 3/8
(E) 2/3

1/6C2=1/15.

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Re: Jack and Jill work at a hospital with 4 other workers. For a  [#permalink]

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25 Oct 2015, 12:35
Bunuel wrote:
atalpanditgmat wrote:
Jack and Jill work at a hospital with 4 other workers. For an internal review, 2 of the 6 workers will be randomly chosen to be interviewed. What is the probability that Jack and Jill will both be chosen?

(A) 1/3
(B) 1/4
(C) 1/15
(D) 3/8
(E) 2/3

1/6C2=1/15.

I just did chance of 1 being selected first time is 1/6 + chance of 1 being selected second time 1/5, turns into 2/30 and reduces to 1/15. Is that the same as 1/6C2=1/15 (my math fundamentals are still lacking a bit)?
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Re: Jack and Jill work at a hospital with 4 other workers. For a  [#permalink]

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25 Oct 2015, 14:07
2
redfield wrote:
Bunuel wrote:
atalpanditgmat wrote:
Jack and Jill work at a hospital with 4 other workers. For an internal review, 2 of the 6 workers will be randomly chosen to be interviewed. What is the probability that Jack and Jill will both be chosen?

(A) 1/3
(B) 1/4
(C) 1/15
(D) 3/8
(E) 2/3

1/6C2=1/15.

I just did chance of 1 being selected first time is 1/6 + chance of 1 being selected second time 1/5, turns into 2/30 and reduces to 1/15. Is that the same as 1/6C2=1/15 (my math fundamentals are still lacking a bit)?

Yes. nCr = n!/(r!*(n-r)!), thus 6C2 = 6!/(2!*4!) = 15

Thus 1/6C2 = 1/15

The correct way to approach is a follows:

Selecting 1 out of the 2 = 2/6 and then the remaining 1 person out of Jack and Jill = 1/5 , giving you the final probability = 2/6*1/5 = 1/15

Hope this helps.
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Posts: 51101
Jack and Jill work at a hospital with 4 other workers. For an internal  [#permalink]

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02 Jun 2016, 03:33
1
Jack and Jill work at a hospital with 4 other workers. For an internal review, 2 of the 6 workers will be randomly chosen to be interviewed. What is the probability that Jack and Jill will both be chosen?

(A) 1/3
(B) 1/4
(C) 1/15
(D) 3/8
(E) 2/3
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Re: Jack and Jill work at a hospital with 4 other workers. For an internal  [#permalink]

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02 Jun 2016, 05:41
3
Bunuel wrote:
Jack and Jill work at a hospital with 4 other workers. For an internal review, 2 of the 6 workers will be randomly chosen to be interviewed. What is the probability that Jack and Jill will both be chosen?

(A) 1/3
(B) 1/4
(C) 1/15
(D) 3/8
(E) 2/3

Total number of ways to choose 2 out of 6 workers= 6!/2!4!= 15

Number of ways to choose both jack and jill= 1

probability= 1/15

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Re: Jack and Jill work at a hospital with 4 other workers. For an internal  [#permalink]

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02 Jun 2016, 10:16
Probability that Jack and Jill will both be chosen out of 6 workers
= (2/6)*(1/5)
= 1/15
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Re: Jack and Jill work at a hospital with 4 other workers. For a  [#permalink]

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03 Aug 2018, 06:50
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