Here, can anyone explain in "Pr[A3|A1(Intersection)A2] = 11/50", how do you interpret A(intersection)B here? I mean if A1 is the event that the first card is heart, and A2 is the event that the second card is heart, what is the intersection of A1 and A2. For me, it just seems that these both events have no intersection.
What the author is saying is that if $A_1$ is the event that the first card is a heart, and $A_2$ is the event that the second card is a heart, then $A_1 \cap A_2$ is the event that both the first and the second cards are hearts. i.e. both events $A_1$ and $A_2$ happen. Does this resolve the problem?
To continue, the probability $P(A_3 \vert A_1 \cap A_2)$ would then be the probability that the third card is a heart, given that both of the first two cards were hearts.