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? \( \frac{1}{8} \) \( \frac{1}{2} \)

When you pick the first card, the probability of drawing a black card (either a spade or a club) is 26 out of 52 cards, which simplifies to \( \frac{1}{2} \). Now for the second card, since we replace the first card, there are still 52 cards in total, and the probability of drawing a heart is 13 out of 52, which again reduces to \( \frac{1}{4} \). When you multiply these probabilities together, you get \( \frac{1}{2} \times \frac{1}{4} = \frac{1}{8} \). So the probability that a black card is chosen first and a heart is chosen second is indeed \( \frac{1}{8} \). Did you know that card games have been around for centuries, evolving into numerous styles and variations? The earliest known deck dates back to 9th century China, and they spread across the globe, leading to games like Poker, Rummy, and Bridge—all fostering social interaction and strategic thinking along the way! For anyone looking to dip their toes into the world of probabilities and card games, start with simple scenarios! Try flipping a coin or rolling dice, and keep track of the outcomes. You can also play classic games like Blackjack or War to apply these concepts in a fun way! Just remember, practice makes perfect and keeps the fun alive!