Two cards are selected without replacement from a standard deck of 52 cards. What is the probability that the first card selected is either red or a face card?

Answer 1

What we don't want is a selection with no face cards or red cards.
If we take all the reds and facecards out, there would be 30 cards left.
so if we find the prob of getting 2 of those cards
= 30/52 x 29/51 = 145/442

So the prob of the stated problem = 1 - 145/442 = 297/442

Answer 2

I misread your question.

It is actually easier than the one I answered.

Since there are 22 cards that are either red or face cards in the deck, the prob(red or face) on the first draw = 22/52 = 11/26

(Why are you stating that there are 2 cards drawn, and why are you stating replacement conditions, if all you are interested in is the first card?)

Answer 3

Thank you! I understand now. The probability is actually 8/13, but you definitely had the right idea. Thanks again!