# Balls drawn without replacement probability question

#### leaning

##### Involved In Discussions
Hello! Can someone check me? My answer is close (.373) but not exact so I'm thinking there's another way this should be done. It doesn't say "exactly one" "or at least one", just "one". I appreciate your help!

A random sample of 5 balls is drawn without replacement from a box that contains 27 black and 3 red balls. What is the probability that the sample contains one red ball?
0.108
0.270
0.369
0.500
C

N= 30 balls
A= 3 red balls
B= 26 black
n=5

C(3,1) x C (27,4)/C(30,5) = 3 x 17750/142506 = .373. Answer should be .369

#### Marc

##### Hunkered Down for the Duration
Staff member
Is it your intent to share here the training materials you are making?

#### leaning

##### Involved In Discussions
Mark,
I think every post I make ends with either 1) a diagram I've pieced together with this group's help that I attach or 2) some other kind of bottom line answer. Is there something in particular you were looking for?

Regards,
John

#### Corca

##### Starting to get Involved
Hello! Can someone check me? My answer is close (.373) but not exact so I'm thinking there's another way this should be done. It doesn't say "exactly one" "or at least one", just "one". I appreciate your help!

A random sample of 5 balls is drawn without replacement from a box that contains 27 black and 3 red balls. What is the probability that the sample contains one red ball?
0.108
0.270
0.369
0.500
C

N= 30 balls
A= 3 red balls
B= 26 black
n=5

C(3,1) x C (27,4)/C(30,5) = 3 x 17750/142506 = .373. Answer should be .369

P = C(27,4) * C(3,1) / C(30,5)

P = 17550 * 3 / 142506

P = 0.369

#### Marc

##### Hunkered Down for the Duration
Staff member
I think every post I make ends with either 1) a diagram I've pieced together with this group's help that I attach or 2) some other kind of bottom line answer. Is there something in particular you were looking for?
Just asking. Since you're putting together a training plan and people here are helping you with a lot of these, I think it will be good if you post (share) what you are writing.

#### leaning

##### Involved In Discussions
Corca: Yep, I re-ran it through the calculator again and got your answer this time. I don't know what happened there.

Here's the final:
Use the combination equation: n!/r!(n-r)!
where N=30, A=3 red balls, B=27 black balls, n=5:
[3!/1!(3-1)! x 27!/4!(27-4)!] / [30!/5!(30-5)!]
(3 x 17550)/ 142506 = 52650/142506 = .3694.

Marc: Look at all my posts. I've shared everything, and I've acknowledged everyone who assisted. I really don't know what else I can do or what you are asking for. If there is some in particular you don't think I've been forthcoming about, please let me know. (???)

Regards,
leaning

Last edited:

#### leaning

##### Involved In Discussions
Found it!

If you do that, you get .373 vice .369.

HA! Cause of mistake identified: Me!

Regards,
leaning

#### Corca

##### Starting to get Involved
LOL we all have similar mistakes.

Good luck.

#### Sharif.Kullab

##### Registered
That one is a nice one

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