Question

two cards are selected from a standard deck of 52 playing cards. the first card is not replaced before the second card is selected. find the probability of selecting a black card and then selecting a red card.

the probability of selecting a black card and then selecting a red card is .
(round to three decimal places as needed.)

Explanation:

Identify the initial composition of the deck

Using the Dependent Events knowledge point

• Total cards: \(52\)
• Black cards: \(26\)
• Red cards: \(26\)

Calculate the probability of selecting a black card first

Using the Dependent Events knowledge point

$$ P(B_1) = \frac{26}{52} = \frac{1}{2} $$

Determine the remaining deck composition and conditional probability

Using the Dependent Events knowledge point

• Remaining total cards: \(51\)
• Remaining red cards: \(26\)

$$ P(R_2 \mid B_1) = \frac{26}{51} $$

Apply the multiplication rule for dependent events

Using the Multiplication Rule for Probability and Dependent Events knowledge points

$$ P(B_1 \text{ and } R_2) = P(B_1) \times P(R_2 \mid B_1) = \frac{1}{2} \times \frac{26}{51} = \frac{13}{51} $$

Convert the fraction to a decimal rounded to three decimal places

Using the Multiplication Rule for Probability knowledge point

$$ \frac{13}{51} \approx 0.25490196... \approx 0.255 $$

Answer:

The probability of selecting a black card and then selecting a red card is <blank>0.255</blank>.
(Round to three decimal places as needed.)