Probability Question

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Probability Question

by seema19 » Mon Sep 26, 2011 3:49 am
Out of 13 applications for a job, there are 5 women and 8 men. It is desired to select 2 persons for the job. The probability that at least one of the selected persons will be a woman is

1) 5/13
2) 14/39
3) 25/39
4) 10/13

Answer: [spoiler]25/39[/spoiler]

This is what I get to know from the question stem:
Out of 5 women and 8 men, we have to select 2 people, out of which at least 1 of the selected person is a woman. The solution states that there are only 2 ways of doing it: (1W and 1M) OR (1M and 1W). My question is: why can I not add one more condition - (2W), so that the answer becomes: (1W and 1M) OR (1M and 1W) OR (2W) ??
Source: — Problem Solving |

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by shankar.ashwin » Mon Sep 26, 2011 4:16 am
I think it includes the case of 2 women as well..

(prob of getting atleast 1 women) = 1 - (Prob of getting both men)

= 1 - (8/13)(7/12)

= 25/39

THis includes the case of having 2 women as well
seema19 wrote:Out of 13 applications for a job, there are 5 women and 8 men. It is desired to select 2 persons for the job. The probability that at least one of the selected persons will be a woman is

1) 5/13
2) 14/39
3) 25/39
4) 10/13

Answer: [spoiler]25/39[/spoiler]

This is what I get to know from the question stem:
Out of 5 women and 8 men, we have to select 2 people, out of which at least 1 of the selected person is a woman. The solution states that there are only 2 ways of doing it: (1W and 1M) OR (1M and 1W). My question is: why can I not add one more condition - (2W), so that the answer becomes: (1W and 1M) OR (1M and 1W) OR (2W) ??

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by user123321 » Mon Sep 26, 2011 4:17 am
one way of doing this is...
1-(probability that if two men are selected for the job)
i.e., 1-(8c2/13c2)
=25/39

user123321