A card is drawn from a standard deck and replaced. After the deck is shuffled, another card is pulled. What is the probability that the first card drawn is a heart and the second card is a diamond? (Enter your probability as a fraction.)
Accepted Solution
A:
Answer:The answer is 1/16.Step by step explanation:We know that a deck has 52 cards, and that the cards are divided into four categories, therefore each type consists of 13 cards.If we’re working with replacement each event is independent to each other, so we’ll use the appropiate formula:P(H∩D) = P(H).P(D)Where:H stands for heart, andD stands for diamonds.The probability that the first card is drawn a heart and the second card is drawn a diamond is equal to the probability that of drawing a heart times the probability of drawing a diamond. We have:P(H) = [tex]\frac{Number of hearts}{Total number of cards}[/tex] = [tex]\frac{13}{52}[/tex] P(D) = [tex]\frac{Number of diamonds}{Total number of cards}[/tex] = [tex]\frac{13}{52}[/tex] ThereforeP(H∩D) = P(H).P(D) = [tex]\frac{13}{52}[/tex].[tex]\frac{13}{52}[/tex] = [tex]\frac{1}{16}[/tex]