# Help needed with probability calculation

Discussion in 'Mathematics' started by geoff1954, Feb 19, 2020.

1. ### geoff1954New commenter

I know it ought to be easy but I can't remember how to do this calculation. Please help. It is a real life problem, not made up for the sake of it. I suspect that some sex discrimination has gone on.

There are twelve applicants for a job, three men and nine women. are six places available. . What is the probability that six women, and no men, are selected for the job (assuming equal probability of all applicants.)

7/8?

3. ### StiltskinStar commenter

Probability of a woman being picked for the first job 9/12
Probability of a woman being picked for the second job 8/11
Probability of a woman being picked for the third job 7/10
Probability of a woman being picked for the forth job 6/9
Probability of a woman being picked for the fifth job 5/8
Probability of a woman being picked for the final job 4/7

Probability of all women getting the jobs roughly 9/100 or 9%

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4. ### geoff1954New commenter

Thanks for the response, but surely it will be much less than 7/8?

5. ### geoff1954New commenter

...........................
That sounds about right. Thanks. So suspicious, but not grounds for action.

6. ### CorvuscoraxStar commenter

I mean against

each candidate has a 50% chance of getting a job. Each man has a 50% chance of getting a job

7. ### catherinedavidNew commenter

If no men are selected in this event, then the chance of all women being picked would surely be 3/4

8. ### StiltskinStar commenter

There are 924 permutations of the candidates (n=12, r=6)

84 of those permutations are all women so 84/924 that all jobs go to women (or 9%)
There is a 100% chance that at least three women will get a job but again only 9% chance all three men would be chosen.

9. ### CorvuscoraxStar commenter

no, it would be 100%

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10. ### StiltskinStar commenter

Theres about a 41% chance there would only be one man chosen and 41% that two men were chosen.

It is possible then that some unconscious bias was involved in selecting who to recruit.

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11. ### GeordieKCOccasional commenter

Probability only tells you how likely an event is to occur. If the probability is greater than zero then that event can occur.

You cannot conclude that a low probability means the event should not occur unless there is bias involved - the probability of a particular person winning the lottery is very small but it still happens

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12. ### bombaysapphireStar commenter

I agree with the 9% calculation but I would be concerned about assuming that all candidates are equally qualified. If just one of the women was clearly outstanding it would mean you were picking for 5 places from 3 men and 5 women and the probability of selecting all women increases to 12%.

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I agree with @Stiltskin's calculation. although it should of course be combination, not permutation. I'm not sure where 7/8 came from.

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14. ### briancantOccasional commenter

(9! x 6!)/(12! x 3!)=0.0909090....

Bet if there was 9 men and 3 women it would have been a bit different.

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