## jesusfreak Group Title 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? 2 years ago 2 years ago

1. ktklown Group Title

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

2. jesusfreak Group Title

Algebra 2

3. ktklown Group Title

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

4. jesusfreak Group Title

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

5. YTheManifold Group Title

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

6. ktklown Group Title

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

7. ktklown Group Title

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

8. cwrw238 Group Title

yes - this a Binomial Probability distribution

9. ktklown Group Title

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

10. jesusfreak Group Title

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

11. jesusfreak Group Title

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

12. ktklown Group Title

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

13. cwrw238 Group Title

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

14. jesusfreak Group Title

Yeah it's 81

15. ktklown Group Title

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

16. jesusfreak Group Title

ok it equals .003969

17. ktklown Group Title

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 Group Title

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 Group Title

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

20. ktklown Group Title

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