What is the probability of a red card or a face card in a standard deck of cards?

Question

What is the probability of a red card or a face card in a standard deck of cards?

Answer 1

Red card 1/2

Face Card 4/13

Either of the two 34/52, or 17/26

Answer 2

A face card is generally assumed to be one depicting a person (namely the Jack, Queen and King).  Thus each suit has 3 face cards.

There are 26 cards in a deck that are red.

Of the black cards, there would be 6 face cards (JQK of clubs, JQK of spades).

All together that is 32 cards that are either red, or face cards out of 52 cards in a deck.

Another way to count this is to count the red cards (26) and the total number of face cards (4 x 3 = 12).  But then subtract the cards that are both red and face cards (6).

26 + 12 - 6 = 32

Fortunately you get the same answer either way.

P(red card or face card) = 32/52 = 8/13 = 0.61538

Alternate method:

P(red card or face card) = P(red card) + P(face card) - P(red card and face card)

= 26/52 + 12/52 - 1/2 * 12/52 = 32/52 = 8/13 = 0.61538

Answer:

Approximately 61.5%

Answer 3

without jokers

probability of a red card is 26/52 which is 1/2 or 50%

probability of a face card (not aces) is 12/52 which is 3/13 or roughly 23%

probability of drawing a red or face card is 32/52 which is 8/13 or roughly 61%

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