Probability Question - Urn problem

[GreenPrint]

Homework Statement

An urn contains 4 white and 4 black balls. We randomly choose 4 balls. IF 2 of them are white and 2 are black, we stop. If not, we replace the balls in the urn and again randomly select 4 balls. this continues until exactly 2 of the 4 chosen are white. What is the probability that we shall make exactly n selections.

Homework Equations

The Attempt at a Solution

I don't see why I can't find the probability of drawing exactly 2 white balls using this method.

(4C2)(4/8)^2(1-4/8)^2
where 4C2 is 4 choose 2

apparently this is wrong but I don't see why. Thanks for any help that you can provide.

 

[Dick]

Homework Statement

An urn contains 4 white and 4 black balls. We randomly choose 4 balls. IF 2 of them are white and 2 are black, we stop. If not, we replace the balls in the urn and again randomly select 4 balls. this continues until exactly 2 of the 4 chosen are white. What is the probability that we shall make exactly n selections.

Homework Equations

The Attempt at a Solution

I don't see why I can't find the probability of drawing exactly 2 white balls using this method.

(4C2)(4/8)^2(1-4/8)^2
where 4C2 is 4 choose 2

apparently this is wrong but I don't see why. Thanks for any help that you can provide.

Well, why do you think it's right? The probability of choosing a white ball is only 1/2 the first time you choose a ball. It's not always 1/2, is it?

 

[GreenPrint]

oh i guess i always assumed you pick the things simultaneously as that's what I've been doing throughout the course so i guess this assumption is wrong?

 

[Dick]

oh i guess i always assumed you pick the things simultaneously as that's what I've been doing throughout the course so i guess this assumption is wrong?

If you pick a white ball first that means there are 3 whites left and 4 blacks. The odds of picking a second white or a black aren't 1/2 anymore. So yes, it's wrong.

 

[Bacle2]

I think it is always useful to describe the sample space: you can succeed the 1st, or the 2nd time, etc.

EDIT: I mean, you can select the two balls in the first trial, or, if you don't, then at the second trial, etc.