# Thread: 15 people (including you) apply for 7 jobs. What are your chances of getting the job?

1. ## 15 people (including you) apply for 7 jobs. What are your chances of getting the job?

Hi

Allow me to extend my thanks to you all for taking the time to visit this thread. I came across this seemingly simple probability question yesterday, but was unsure of the answer.

The question: 15 people (including you) apply for 7 jobs. What are your chances of getting the job?

My reasoning is as follows:

You have a sample set of 15 people. There are 7 events (selections). Intuition lead me to p(E) = 7/15. However, this answer seemed too easy.

I thought of viewing the 7 events separately. The probability that you will get the first slot (job) is 1/15. After that, the sample set is reduced to 14. Therefore, the probability that you will get the second slot is 1/14. And so on, as such:

1/15 + 1/14 + 1/13 + 1/12 + 1/11 + 1/10 + 1/9 = 60%

In the end, however, I'm unsure if my approach is correct. It's been a long time since discrete math Thank you all in advance.

2. ## Re: 15 people (including you) apply for 7 jobs. What are your chances of getting the

Assuming the chances are purely random (which they are not) your approach is correct. If you were talking about picking colored marbles I'd say that's a sound approach, however be warned that applying for and obtaining a job has little to do with chance and everything to do with perception. If you (and I'm not saying you cridex) smell offensively bad then the probability of you getting a job is effectively 0. There is a volume of research on this topic but that depends on how interested you are in this.

3. ## Re: 15 people (including you) apply for 7 jobs. What are your chances of getting the

As per your logic suppose there are 15 jobs then the probability is
1/15 + 1/14 + 1/13 + 1/12 + 1/11 + 1/10 + 1/9 ... 1/2+1/1 > 100%

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trinker (12-29-2011)

5. ## Re: 15 people (including you) apply for 7 jobs. What are your chances of getting the

true hadn't thought of that.

6. ## Re: 15 people (including you) apply for 7 jobs. What are your chances of getting the

I was thinking there should be some combinatorics in here. For example, there are N total combinations and k of them meet the criteria (that is, k combinations include me as one of the 7 candidates chosen). I'm unsure how to calculate k.

I think that N should be 15 choose 7, or 6435.
C(15,7) = n! / (n - k)! * k!
C(15,7) = 15! / ((15 - 7)! * 7!)
C(15,7) = 6535

7. ## Re: 15 people (including you) apply for 7 jobs. What are your chances of getting the

It might work to think about the probability of not getting the job. Not necessarily using combinatorics.

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cridex (12-29-2011)

9. ## Re: 15 people (including you) apply for 7 jobs. What are your chances of getting the

looks tricky but i think your first approach is ok. as easy as it looks, i would go for 7/15.

10. ## Re: 15 people (including you) apply for 7 jobs. What are your chances of getting the

Do you have justification for 7/15? There is and it's a relatively simple argument but without justification it's not a good answer to help somebody understand the answer.

11. ## Re: 15 people (including you) apply for 7 jobs. What are your chances of getting the

Originally Posted by Mukubuta Mubiana
looks tricky but i think your first approach is ok. as easy as it looks, i would go for 7/15.
Agree with Dason. I'd love to see a proof !

12. ## Re: 15 people (including you) apply for 7 jobs. What are your chances of getting the

Originally Posted by cridex
Agree with Dason. I'd love to see a proof !
The proof is quite easy - I was hoping the poster would show their proof though if they have one. Mine is just a symmetry argument.

13. ## Re: 15 people (including you) apply for 7 jobs. What are your chances of getting the

Originally Posted by Dason
The proof is quite easy - I was hoping the poster would show their proof though if they have one. Mine is just a symmetry argument.
I cordially invite you to post it

14. ## Re: 15 people (including you) apply for 7 jobs. What are your chances of getting the

Well the way I was implying to do it in my first post was to calculate the probability you don't get a job. Imagine the job offers are ordered. So the first job comes and if everybody is equally likely to get the job then there is a 14/15 probability you don't get the job. Drat! The second job comes and now there are only 14 candidates which means there is a 13/14 probability you don't get the job. So on and so on. Multiply those together and you get . But that's the probability we don't get a job so is the probability of getting a job.

A nicer argument is just by symmetry. Everybody is equally likely to get any of the jobs. 7/15 people will get a job. Therefore the probability any one person gets a job is 7/15.

15. ## The Following User Says Thank You to Dason For This Useful Post:

cridex (12-29-2011)

16. ## Re: 15 people (including you) apply for 7 jobs. What are your chances of getting the

Thanks, Dason. I can't believe it is just that simple.... I stumbled across this question on an employer entrance exam. 7/15 was not one of the multiple choice answers [edit: answers, not questions!], so I either misunderstood the question or they didn't list the correct answer. There was no "None of the above" answer in the selection. Luckily I got a 93% on the exam (26 of 28 questions).

17. ## Re: 15 people (including you) apply for 7 jobs. What are your chances of getting the

Well the exact wording can change quite a bit. For instance I assumed that "What are the chances of getting the job" meant "What is the probability of getting a job assuming everybody is equally likely to get any of the jobs and if you get offered one job you won't get offered another".

18. ## Re: 15 people (including you) apply for 7 jobs. What are your chances of getting the

Originally Posted by Dason
Well the exact wording can change quite a bit. For instance I assumed that "What are the chances of getting the job" meant "What is the probability of getting a job assuming everybody is equally likely to get any of the jobs and if you get offered one job you won't get offered another".
That's the way I interpreted it, as well. It wasn't specified whether the odds were equal between candidates or not, I had to assume they were equal.

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