SOLUTION: In an ordinary deck of 52 cards, how many cards are either RED or FACE CARDS?

Question 958153: In an ordinary deck of 52 cards, how many cards are either RED or FACE CARDS?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the formula used is:

p(A or B) = p(A) + p(B) - p(A and B)

p(A and B) means the probability of both A and B occurring at the same time.

you have 52 cards in the deck.

26 of the cards are red (either diamonds or hearts).

There are 12 face cards in the deck.

They are:

4 Kings
4 Queens
4 Jacks

6 of the face cards are red (diamonds or hearts) and 6 of the face cards are black (spaces or clubs).

let A be the event that you have a red card.

Since there are 26 red cards in the deck, then p(A) = 26/52.

let B be the event that you have a face card.

Since there are 12 face cards in the deck, then p(B) = 12/52.

let A and B be the event that you have cards that are both red and face cards.

Since there are 6 red face cards in the deck, then p(A and B) = 6/52.

p(A) + p(B) - p(A and B) is therefore equal to 26/52 + 12/52 - 6/52 = 32/52.

the probability that you will have a red card or a face card is equal to 32/52.

Why did we subtract the cards that are red and face cards at the same time?

Because, if we didn't, they would be double counted.

They would be counted as red cards and they would be counted again as face cards.

Since they are the same card, we needed to remove the double counting which is why we subtracted the number of cards that were both red and face cards at the same time.

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