Selecting from an Urn. Conditional probability

[torquerotates]

Homework Statement

A box contains 4 red balls and 6 white balls. A sample size of 3 is drawn without replacement from the box. What is the probability of obtaining 1 red ball and 2 white balls given that at least 2 of the balls in the sample are white?

Homework Equations

The Attempt at a Solution

Well if I got at least two white balls that means that I either have 2W or 3W. If I have 2W, then I can chose among the remaining 4W and 4R. Hence the probability is 1/2 given that i already otained 2W. If i have 3W, the probability is 0 given that i already obtained 2W. Hence my answer is 1/2. BUT... I am wrong. the answer is 3/4. I am not sure where i went wrong here.

 

[tiny-tim]

hi torquerotates!

What is the probability of obtaining 1 red ball and 2 white balls given that at least 2 of the balls in the sample are white?
…
If I have 2W, then I can chose …

no, that's if the question says "given that the first 2 of the balls in the sample are white"

(or any particular pair)

find P(W ≥ 2) and P(W = 2) ​