In a standard deck of 52 cards, what is the probability of drawing one card that is not a club and not a face card?

Question

Probability: unions and intersections

Answer 1

You have 52 cards total.  If you take out the clubs, you then have 39 cards remaining.  Now of those 39, you need to remove all face cards from that subset.  That means you must remove the Jack, Queen, and King from the other three suits.  That's 9 cards, leaving you with 30.  Accordingly, the odds are:

 

30/52

Answer 2

Hello, thank you for taking the time to post your question!

There are 13 clubs in the deck and 12 face cards (Jack, Queen, and King for each of the suits), but in doing your calculation you want to subtract off “3” because you don’t want to double count the Jack, Queen, and King of Clubs.

So there ends up being

13 + 12 – 3 = 22 cards out of the 52 that meet the criteria of being a club or a face card

The question then is asking about the probability of NOT drawing one of those cards, meaning that you want to take

(52 – 22) / 52 = 30/52 = 0.577

I hope that helps you get moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)