## Pulsified333 one year ago Assume that you have 5 red balls and 4 blue balls from which randomly to select two without replacement. (1) What is the probability that exactly one red ball is chosen? (2) What is the probability that the second ball is blue given that at least one of the balls is blue?

1. anonymous

there are a couple ways to do this perhaps the most intuitive way is to calculate the probability that the first ball is red and the second is not then the probability that the first is not red, and the second is do you know how to do that?

2. Pulsified333

i just got the first part but the second part I'm not sure how to do

3. anonymous

guess we need some notation

4. anonymous

actually a diagram would be bets lets see if i can draw one

5. Pulsified333

ok

6. anonymous

actually no, lets just do it easy you have already computed the probability that exactly one ball is blue right?

7. anonymous

what did you get, and how did you do it?

8. Pulsified333

I got 5/9

9. anonymous

the probability that both balls are blue is $\frac{4}{9}\times \frac{3}{8}=\frac{1}{6}$

10. anonymous

the probability that the first is blue and the second is red is $\frac{4}{9}\times \frac{5}{8}=\frac{5}{18}$

11. anonymous

and the probability that the first is red and the second is blue is the same $\frac{5}{18}$ add these up to get the probability that at least one is blue

12. anonymous

you need that for your denominator

13. Pulsified333

so 1/6+5/18

14. anonymous

no it is $\frac{1}{6}+\frac{5}{18}+\frac{5}{18}$

15. Pulsified333

oh

16. Pulsified333

17. anonymous

ok good so that is your denominator

18. anonymous

your numerator is the probability that the second ball is blue

19. Pulsified333

so 4/9

20. anonymous

yes

21. Pulsified333

8/13?

22. anonymous

that is what i get, yes

23. Pulsified333

:D it was right thanks man.

24. anonymous

yw nothing like instant gratification !

25. Pulsified333

btw if i want to send you a message how do i do that?

26. anonymous

you cannot

27. Pulsified333

;(

28. anonymous

you can tag me in a question if you like @satellite73

29. Pulsified333

okay I'm going to be posting a lot of problems tonight because I have a midterm tomorrow that I have not even studied for yet and I pulled an all nighter last night to work on a presentation that I had to present today and study for a test that i took today.

30. anonymous

yikes

31. Pulsified333

@satellite73 I know. Right now I'm scared that I am going to have to stop doing my math hw and study for the test and take the fail on the hw