## anonymous 4 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. anonymous

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

2. anonymous

Algebra 2

3. anonymous

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

4. anonymous

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

5. anonymous

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

6. anonymous

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

7. anonymous

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

8. cwrw238

yes - this a Binomial Probability distribution

9. anonymous

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

10. anonymous

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

11. anonymous

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

12. anonymous

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. anonymous

Yeah it's 81

15. anonymous

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

16. anonymous

ok it equals .003969

17. anonymous

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. anonymous

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. anonymous

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

20. anonymous

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