Probability – Calculating the Probability of Choosing the King of Hearts Given That There is a King

card-gamesprobability

I am currently stuck on this question and how it would be worked out.

I currently have the probaility that at least one king will be 0.341

And that the probability of drawing a King of hearts is 51 c 1 / 52 c 5 [editted! I typed it wrong 51 c 4 / 52 c 5]

But the following question is stumping me a bit,

A hand of five cards is dealt from a normal pack of 52 cards. Find the probability that the hand will contain the king of hearts, given that there is at least one king.

Thanks,

Best Answer

HINT: There are $\binom{48}5$ hands with no king, so there are $\binom{52}5-\binom{48}5$ hands with at least one king. There are $\binom{51}4$ hands that contain the king of hearts. Can you put those pieces together to get the desired probability?