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

Answer:

Option B.

Step-by-step 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 = $\frac{13}{52}$

The probability of choosing second card is spade = P₂ = $\frac{13}{51}$

Probability = P₁ × P₂

$=\frac{13}{52}\times\frac{13}{51}$

$=\frac{169}{2652}$

$=\frac{13}{204}$

The probability of choosing one club and one spade is $\frac{13}{204}$.