Question

Two cards are drawn without replacement from a standard deck of 5252 playing cards. What is the probability of choosing a heart and then, without replacement, a spade? Express your answer as a fraction or a decimal number rounded to four decimal places

Answer 1

Answer:

$\frac{13}{204}$ ≈ 0.0637

Step-by-step explanation:

Given: Two cards are drawn without replacement from a standard deck of 52 playing cards.

To find: probability of choosing a heart and then, without replacement, a spade

Solution:

Probability refers to chance of occurrence of any event.

Probability = Number of favorable outcomes ÷ Total number of outcomes

Total number of cards = 52

Number of hearts = 13

So,

probability of choosing a heart = $\frac{13}{52}=\frac{1}{4}$

Number of remaining cards = $52-1=51$

Number of spades = 13

Probability of choosing a spade = $\frac{13}{51}$

Events consisting of choosing a heart and spade are independent.

So,

Probability of choosing a heart and then, without replacement, a spade =

Probability of choosing a heart × Probability of choosing a spade

= $\frac{1}{4}(\frac{13}{51})=\frac{13}{204}$ ≈ 0.0637