How should I understand conditional probability?

conditional-probability

Solution 1:

What is A⋂B in this case?

I you have 3 marbles, R,B and Y and you pick two you can have the following sample space

$$\{RB,RY,BR,BY,YR,YB\}$$

thus in your case, $A\cap B$ is the event $BR$ with probability $\frac{1}{3}\cdot\frac{1}{2}$

as you can argue, any events among the 6 possible are equiprobable, with probability $\frac{1}{6}$

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