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, without replacement. What is the probability of choosing one club and one spade?

A. 1/2
B. 13/204
C. 25/102
D. 13/102

Answer 1

Option B.

Explanation:

There are 13 cards of club and 13 cards of spade in a standard deck of playing cards.

Total cards in a deck of playing cards = 52

The probability of choosing first card is club P₁ =
`(13)/(52)`

The probability of choosing second card is spade = P₂ =
`(13)/(51)`

Probability = P₁ × P₂

`=(13)/(52)*(13)/(51)`

`=(169)/(2652)`

`=(13)/(204)`

The probability of choosing one club and one spade is
`(13)/(204)`.