anonymous 5 years ago In a sample of 26 hand-held calculators, 20 are known to be nonfunctional. If 6 of these calculators are selected at random, what is the probability that exactly 4 in the selection are nonfunctional? Round to the nearest thousandth. A. 0.667 B. 0.316 C. 0.769 D. 0.300 E. 0

1. anonymous

Draw a probability tree. I would, but I don;t have the patience, and hate statistics with a passion.

2. amistre64

I know you have a 76.9% chance of picking one the first time..... but what to do after than I would have to read up on :)

3. amistre64

I would assume our initial options would lead to these b,b,b,b,b,b b,b,b,b,b,g b,b,b,b,g,g b,b,b,g,g,g b,b,g,g,g,g b,g,g,g,g,g g,g,g,g,g,g

4. anonymous

$\frac{20 \times 19 \times 18 \times 17 \times 6 \times 5}{26 \times 25 \times 24 \times 23 \times 22 \times 21} \times ^6 C_4$

5. anonymous

Well I tried that but that doesn't get me close to any of the solutions?

6. anonymous

Of course it does, I just told you it.

7. anonymous

Do you know what 6C4 means?

8. anonymous

$^NC_R \equiv \frac{n!}{n!(n-r)!}$

9. anonymous

Yes lol sorry I think I just plugged in my calc wrong was all! Thanks a bunch!

10. anonymous

You have to explain to me why that is the answer now, though.

11. amistre64

20/26; then the odds go to 19/25, then to 18/24 .....

12. anonymous

My definition of NCR has n! on the bottom when it should be r!, apologies to anyone confused.

13. anonymous

well the equation you just gave me is saying the number of combinations of n elements taken r times

14. amistre64

thats last bit is combinatorical .... i think

15. anonymous

Ya I'm pretty sure it is combinatorical just not positive on how to solve it via the way my book is showing me lol

16. anonymous

Sort of - You need to pick 4 non functioning, and 2 functioning. The first one gives you the overall odds of each in turn, and the second gives you the different orders you can do it in.

17. anonymous

uh ok I'm confused again.... Can you show me on http://www.dabbleboard.com/draw?b=Guest644716&i=0&c=3327a9e1158d904a38fbad735c24ed28cad7bcd9

18. anonymous

No, sorry, I have stuff to do. Draw a probability tree.

19. anonymous

ok Thanks for helping though! Much appreciated... I'll mess around with it until I figure it out:)

20. anonymous

amistre64....what were you trying to say when you posted...20/26; then the odds go to 19/25, then to 18/24? if I keep working my way down what does that do?

21. anonymous

amistre64....what were you trying to say when you posted...20/26; then the odds go to 19/25, then to 18/24? if I keep working my way down what does that do?

22. anonymous

Let's say you choose FFFFNN, the odds are: (20/26 x 19/25 x 18/24 x 17/23) x (6/22 x 5/21) However, you could actually do this in any order, so you have to multiply it by 6C2