# Probability question -

Teacher's questions

### Probability question -

Hi folks - I need some help with a tricky probability. Here's the situation:

Let's say there are 4M internet users in Age Group A. (The total set)
Of those 4M, there are 1,000 users who play a specific sport.
Those 1,000 are spread evenly over 125 teams, so 8 players each.

1. What's the probability of selecting 3 random users (from the 4M) who all play that sport?
2. What's the probability of all 3 users being members of the same team?

This isn't a school problem - I'm a 47 year old writer, and I need to figure out this absurdly improbable number. (The improbability is the point.) Any advice / guidance / direction here would be appreciated! (I have a moderate familiarity with combinations & permutations, and their notations, so do feel free to use whatever formulae / notations are needed.)

Any questions, please feel free to let me know. Thanks! ~ MW.
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### Re: Probability question -

I take it that "3M" means 3,000,000.

Also you say "selecting 3 random users" but I believe you mean 3 specific users, chosen randomly.

The probability of choosing one specific user from 3,000,000 is 1/3000000. The probability of choosing another specific person from the remaining 2,999,999 is 1/2999999. The probability of choosing a third specific person from the remaining 2,999,998 is 1/2999998. The probability of randomly choosing three specific people out of 3,000,000 is the product of those, 1/[(3000000)(2999999)(2999998)]. That's very small!

Given that you have chosen the three, the first person is on one of the teams. The progability that the second person chosen is also on that team is 1/7 and the probability the third person is also on that team is 1/6. The probabililty all three people chosen are on the same team is (1/7)(1/6)= 1/42.
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