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

≈ 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 =

Number of remaining cards =

Number of spades = 13

Probability of choosing a spade =

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

= ≈ 0.0637

for this case we must apply distributive property to the following expression:

the distributive property states that:

then, when applying the property we have to multiply the -2 for each term within the parenthesis:

60 for the first and 130 for the second

step-by-step explanation: