Four cards are randomly chosen (without replacement) from a deck of 52 cards. Let K be the event that two of the four cards are King and the other two are Aces. Let E be the event that one of the four cards is a King of Hearts. The conditional probability P(K | E) is equal to ?

Question

kropot72 · Answer

I have got as far as
$$P(K|E)=\frac{K \cap E)}{P(E)}$$
But how do I calculate K intersection E?

anonymous · Answer

the intersection of K and E means two are aces, one is the king of  hearts and one is some other king

anonymous · Answer

i think there are 18 ways to get this, 
$$\binom{4}{2}\times 3$$

anonymous · Answer

number of ways to get 2 aces and 2 kings is 
$$\binom{4}{2}\times \binom{4}{2}=6\times 6=36$$

anonymous · Answer

a simpler way to think of it is off all the possibilities with two aces and two kings, half of them have the king of hearts

kropot72 · Answer

Many thanks for your explanation which is clearing my mind on this one. I will try taking it from this point. Thank you again for your attention. :)