# Combinatorics

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• Jul 27th 2008, 03:29 PM
user_name
Combinatorics
We have a bowl, inside of which are 6 balls.

5 of them are black. 1 of them is white.

We pull out 1 ball from the basket. Then we return the ball to the basket.

We repeat this 8 times.

What is the probability we pulled out a black ball precisley 4 times and pulled out a white ball precisley 4 times?

Thanks
• Jul 27th 2008, 03:47 PM
Plato
Quote:

Originally Posted by user_name
We have a bowl, inside of which are 6 balls. 5 of them are black. 1 of them is white. We pull out 1 ball from the basket. Then we return the ball to the basket. We repeat this 8 times.
What is the probability we pulled out a black ball precisely 4 times and pulled out a white ball precisley 4 times?

Because the drawn ball is returned, it is the same on every draw. Therefore the events are independent and are modeled by binominal distribution. Then p= 1/6 & N=8. So C(8,4)[(1/6)^4][(5/6)^4].
• Jul 27th 2008, 03:54 PM
user_name
Ah, binominal!

I knew I was missing something fairly obvious, but couldn`t figure out what.

Cheers, mate.