Question

three cards are drawn with replacement from a standard deck. what is the probability that the first card will be a heart, the second card will be a red card, and the third card will be an ace?

Answer 1

The probability of drawing a heart, then a red card, and then an ace with replacement from a standard deck is 0.24%.

Step-by-step explanation:

The question asks about the probability of drawing three specific types of cards from a standard deck of 52 playing cards using sampling with replacement. The events described are drawing a heart as the first card, a red card as the second card, and an ace as the third card.

The probability of drawing a heart first is 13/52 since there are 13 hearts in a deck. Since the second card needs to be red and there are 26 red cards in a deck (hearts and diamonds), the probability is 26/52. For the third card to be an ace, the probability is 4/52 as there are 4 aces in a deck.

Since each draw is independent (because of sampling with replacement), we multiply these probabilities together:

• Probability of first card being a heart: 13/52
• Probability of second card being red: 26/52
• Probability of third card being an ace: 4/52

So, the overall probability is (13/52) * (26/52) * (4/52) = 338/140608 ≈ 0.0024 or 0.24%.