Question

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?

Answer 1

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?

Answer 2

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

Answer 3

guess we need some notation

Answer 4

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

Answer 5

ok

Answer 6

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

Answer 7

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

Answer 8

I got 5/9

Answer 9

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

Answer 10

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

Answer 11

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

Answer 12

you need that for your denominator

Answer 13

so 1/6+5/18

Answer 14

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

Answer 15

oh

Answer 16

the answer would be 13/18

Answer 17

ok good so that is your denominator

Answer 18

your numerator is the probability that the second ball is blue

Answer 19

so 4/9

Answer 20

yes

Answer 21

8/13?

Answer 22

that is what i get, yes

Answer 23

:D it was right thanks man.

Answer 24

yw
nothing like instant gratification !

Answer 25

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

Answer 26

you cannot

Answer 27

;(

Answer 28

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

Answer 29

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.

Answer 30

yikes

Answer 31

@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