Probability Help?

[BGboothA]

OK you Degens ain't the smartest cats in the book, but you know your probability and odds.

I need the EQUATION for this NOT the answer!

If you have 7 rocks, 2 black and 5 blue. what are the odds you would pull the 2 black rocks with 4 chances.

Same thing with 8 rocks with 2 black and 6 blue.

10 points to the first person to help a brother out.

[BGboothA]

Damn I thought this would have been a quick one?

[matthew919]

I'll assume there's no replacement. The answer in the first case is 2/7.

Total number of ways to select 4 rocks out of 7 (regardless of color) is 7 choose 4, or 7!/4!(7-4)! = 35.
Now the number of ways to successfully choose exactly 2 black and 2 blue is 5 choose 2 times 2 choose 2, or:
(5!/2!(5-2)!)*(2!/2!(2-2)!) = 10*1 = 10.

Since the probability is number of possible successes / total possibilities, we have: 10/35 = 2/7.

Similarly, the answer for the second case is 15/70, or 3/14.

[BGboothA]

Thanks for the response....I understand the answer, but the equation is still a miss to me.

Big picture: I am working an excel file and need to write a script that allows me to figure this out (always picking 4 stones and needed 2 black and 2 blue) The number of overall stones change, but there are always only 2 black ones. The are blue.

If you had to write teh same equation knowing there are always 2 black stones and represent total number of stones as "X" lets say....how would that look?

[rfr3sh]

if there is replacement you could use binomial distribution i believe otherwise do what matt said

[BGboothA]

correct no replacement

[matthew919]

If these assumptions always hold, you can essentially forget about one of the combination terms in the numerator, since it will reduce to 1. The denominator will be X choose 4, and the simplified numerator will be (X-2) choose 2.

After combining like terms, and simplifying, you get:

12/(X(X-1)).

Hope this helps.

Matt

[BGboothA]

Thank you! OK, I think I get it....I am going to test it out and see what I can figure out.

[hokim]

To make mathew919's formula simple, the probability is (2C2*5C2)/7C4 = 2/7

, where C stands for combination, which is combin() in excel.