An urn contains $10$ black and $5$ white balls. Two black balls are drawn from the urn and one after other. $E$ and $F$ denote respectively the events that first and second ball drawn are black.
How do I find $P(F|E)$?
I think $P(F|E) =$ the probability of occurrence of $F$ when $E$ is taken as sample space. When $E$ took place we had a black ball which should now be sample space for $F$. So, now $P(F|E)$ should be $1$. But book says $P(F|E) = 9/14$. where am I wrong.
In all questions I did in previous exercise of my book I used $P(A|B) =$ Probability of occurrence of $A$ when $B$ is taken as sample space. So if I already have done event $E$, now I should have only a black ball in my hand. Now $P(F|E)$ should mean I take out next black black ball from my black ball obtained in $E$. This gives probability of $1$. Another way to find $P(F|E)$ can be by $n\left\lvert F \cap E\right\lvert / n\left\lvert E \right\lvert$ . Can you please explain using this method?