I have a question that is asking the probability of the intersection and union of two cases. The question assumes you are drawing 5 cards from a deck of 52.
A: Drawing at least 3 hearts
B: Drawing at most 1 King
I have solved the two as
$P(A)\frac{\binom{13}{4}\binom{39}{1}}{\binom{52}{5}}+\frac{\binom{13}{3}\binom{39}{2}}{\binom{52}{5}}+\frac{\binom{13}{5}}{\binom{52}{5}}=9.28\%$ and
$P(B)\frac{\binom{4}{1}\binom{48}{4}}{\binom{52}{5}}+\frac{\binom{48}{5}}{\binom{52}{5}}=95.83\%$
So now I cannot quite figure out how to $P(A\cap B)$ and $P(A\cup B)$. For $P(A\cap B)$ I am not sure what $P(B|A)$ would be. I know there are two cases:
- Three hearts and NO kings
- Three hearts and ONE king
If anyone can provide some pointers it would be very appreciated.