# Conditional probability question concerning cards

A card is drawn from a standard pack. The dealer tells the players that it is a court card (jack, queen, king). what is the probability that it is either a jack or a red card? I've been stuck on this question since yesterday and I just feel like I still don't thoroughly understand this topic and that is why I cannot solve this problem. Could someone please explain clearly the concept of conditional probability to me and give me a hint on how to solve this question. I've tried tons of methods but still, I cannot get 2/3 which is the correct answer

Thank you so much for your help

We are told the card is a "court card" (commonly called a "face card" in the west). This allows us to effectively pretend that we are working with a much smaller deck, one that has only the twelve court cards in it and no other cards.

What is the probability that it is a jack?

$$\frac{1}{3}$$

What is the probability that it is red?

$$\frac{1}{2}$$

Now, remember your inclusion-exclusion principle... $$Pr(A\cup B) = Pr(A)+Pr(B)-Pr(A\cap B)$$

What information are we still missing? Plugging in everything, what do we get as a final result?

We still needed to find the probability that it is a red jack., that would be $$\frac{1}{6}$$ and so plugging everything in we get the probability it is red or a jack would be $$\frac{1}{3}+\frac{1}{2}-\frac{1}{6} = \frac{2}{3}$$

• Wow, thank you so much for your help – BooScout Sep 5 '19 at 1:14