Question

1. one card from a deck of cards is selected, it is replaced, and another card is chosen. what is the probability that the first card is a black card and the second is a red card?

Explanation:

Step1: Probability of black card

A standard deck has 52 cards, 26 black. Probability:
$P(\text{black}) = \frac{26}{52} = \frac{1}{2}$

Step2: Probability of red card

With replacement, deck is unchanged. 26 red cards. Probability:
$P(\text{red}) = \frac{26}{52} = \frac{1}{2}$

Step3: Multiply independent probabilities

Since draws are independent, multiply the two probabilities:
$P(\text{black then red}) = \frac{1}{2} \times \frac{1}{2}$

Answer:

$\frac{1}{4}$