## jesusfreak 3 years ago the principal will randomly choose 6 students from a large school to represent the school in a newspaper photograph. the probability that a chose student is an athlete is 30%. (assume that this doesn't change) What is the probability that 4 athletes are chosen?

1. ktklown

Is this for a statistics class, or something like algebra?

2. jesusfreak

Algebra 2

3. ktklown

YTheManifold: that's not actually correct because you're not including the degree of freedom that any 4 can be chosen

4. jesusfreak

Would you like to see what the possible answers could be?

5. YTheManifold

Sorry ${6\choose 4}\cdot 0.3^4\cdot 0.7^2$ of course

6. ktklown

.3^4 * .7^2 is the p^k and p^(n-k) but you need the (6 choose 4) as well.

7. ktklown

the formula YTheManifold just posted is correct - can you compute that, jesusfreak?

8. cwrw238

yes - this a Binomial Probability distribution

9. ktklown

the general form is (n choose k) * p^k * p^(n-k). (typo in the previous one)

10. jesusfreak

It all looks like gibberish. I have no idea what to do.

11. jesusfreak

The answers it gives is 0.05, 0.06, 0.07, 0.08

12. ktklown

OK, let's go through it step by step. Do you know how to compute .3^4?

13. cwrw238

th 6 4 part means the number combinations of 4 from 6

14. jesusfreak

Yeah it's 81

15. ktklown

You forgot the decimal -- it's 0.3^4 we're computing. Then multiply that by 0.7^2.

16. jesusfreak

ok it equals .003969

17. ktklown

yes! Now you just need to multiply that by the (6 4) part, and you'll be done. That's called a "binomial". It's pronounced "6 choose 4", which means, if you have 6 things, how many ways can you choose 4 of them?

18. ktklown

There's a formula for computing that, but a lot of people just type it into a calculator - it's 15 in this case.

19. ktklown

The formula is n! / ( k! * (n-k)! )

20. ktklown

Anyway so in this case just multiply 15 * .3^4 * .7^2 and that's your answer.