Question

in a standard deck of cards there are 13 spades, 13 clubs, 13 hearts, and 13 diamonds. the spades and the clubs are black and the hearts and the diamonds are red.

if two cards are chosen at random from a deck, one at a time, and replaced after each pick, what is the probability that a black card is chosen first and a heart is chosen second?

\\(\frac{1}{8}\\)

\\(\frac{1}{2}\\)

\\(\frac{2}{3}\\)

\\(\frac{3}{4}\\)

Explanation:

Calculate the total number of cards and black cards

Using the Theoretical Probability knowledge point

$$
LATEXBLOCK0
$$

Calculate the probability of choosing a heart second

Using the Theoretical Probability knowledge point

$$
LATEXBLOCK1
$$

Calculate the joint probability of both independent events

Using the Independent Events and Probability Multiplication Rule knowledge points

$$
LATEXBLOCK2
$$

Answer:

• (A) \(\frac{1}{8}\) (Correct answer)
• (B) \(\frac{1}{2}\)
• (C) \(\frac{2}{3}\)
• (D) \(\frac{3}{4}\)