Question

A standard deck of playing cards has 13 cards in each of four suits: hearts, clubs, diamonds, and spades. Two cards are chosen from the deck at random. What is the probability of choosing one club and one spade?

a 1/2

b 13/204

c 13/102

d 15/102

Answer 1

C

Explanation:

13C1 × 13C1 / 52C2

169/1326

13/102

Answer 2

13/102

Explanation:

We will assume that order doesn't matter

P (club) = number of clubs / total

13/52

Now we have 51 cards since we keep the card

P ( spade) = number of spades / total

13/51

P(club, keep, spade) = 13/52 * 13/51 =13/204

But we also have the case of spade, club

P (spade) = number of spade / total

13/52

Now we have 51 cards since we keep the card

P ( club) = number of clubs / total

13/51

P(spade, keep, club) = 13/52 * 13/51 =13/204

Add the two together since it can be in either order

13/204+13/204

26/204 = 13/102