A bag contains three red balls, three black balls, and three blue balls. You pick two balls at random (without replacement). Given that you pick two balls with the same colour, what is the probability that they are blue?
I let A be the event 'you pick 2 balls of the same colour' and I let B be the event 'you pick to blue balls'
To work out P(B|A), first I tried to find the P(A), which I believe is 3/9*1/2 however, I'm unsure what to do after.
$$P(B|A)=\frac{P(B\cap A)}{P(A)}=\frac{\frac{3}{9}\times \frac{2}{8}}{3\times\frac{3}{9}\times\frac{2}{8}}$$
$P(A)$ is the probability of two balls are same color
$P(B)$ is the probability of two balls are blue