Question

A card is drawn at random from a well shuffled pack of 52 cards.Find the probability that the card drawn is a red card.

Answer 1

There are 4 face cards in every set of (hearts, spades, diamonds, clover). Moreover, there are 26 red cards and 26 black cards. With these facts, I have 26 red cards, but I know 4 red diamonds and 4 red hearts are in there.

So, 4/52 +4/52 red face cards in the deck. That is, the probability of getting one red face card from a deck of 52 cards is 8/52. But when we get the second card, we are getting it from a deck of, now, 51 cards. with this same idea above, without replacement, we have 7/51 probability for our second card.

We want the probability of one red face card (A) AND another red face card (B) from the deck of 52 cards. That is, P(A AND B) = P(A) * P(B|A).

So, P(A AND B) = 8/52 * 7/51 = 0.02111613876

Answer 2

You could count the number of red cards (26) and then divide by the total number of cards (52) to get 1/2.