Use Bayes' theorem. Let A=1st ball is green, B=2nd ball is green, then
P(A|B)=P(B|A)P(A)/P(B)
P(A)=1/3(1+1/2), P(B)=1/3, P(A|B)=1 so
P(B|A)=(1x1/3)/(1/3(3/2))=2/3.
Use Bayes' theorem. Let A=1st ball is green, B=2nd ball is green, then
P(A|B)=P(B|A)P(A)/P(B)
P(A)=1/3(1+1/2), P(B)=1/3, P(A|B)=1 so
P(B|A)=(1x1/3)/(1/3(3/2))=2/3.
13% chance that it will be 50% green balls
>have 2 possible boxes
>1 has a red ball and 1 has a green ball
>1/2 of the balls are green
>1/2 is 50%
>some retard did all that math and got 2/3 instead
I fucking hate french people
With only the information that you've picked a green ball, it's twice as likely that you're taking from the two green ball box than the one with a green and a red. On average, two out of every three green balls you pick will be from the two green ball box.
50%
Either the ball is green or it isn't
The fact that there's two possibilities doesn't mean that they're equally likely
It's almost as if probabilities aren't as intuitive as you'd think they are.