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 a queen?

Answer 1

The probability of drawing a heart, a red card, and a queen with replacement from a standard deck of cards is 1/52.

Step-by-step explanation:

To find the probability of drawing a heart, a red card, and a queen with replacement, we need to break down the problem into separate probabilities.

1. The probability of drawing a heart on the first draw is 13/52 (since there are 13 hearts in a deck of 52).
2. The probability of drawing a red card on the second draw is 26/52, as half of the deck is red.
3. The probability of drawing a queen on the third draw is 4/52, as there are 4 queens in the deck.

To find the overall probability, we multiply these individual probabilities together. So the probability of drawing a heart, a red card, and a queen with replacement is (13/52) * (26/52) * (4/52) = 1/52.

Answer 2

The probability of drawing a heart, then a red card, and then a queen with replacement from a standard deck is 1/104.

Step-by-step explanation:

The question involves calculating the probability of drawing specific cards from a standard deck in sequence with replacement. To find the probability that the first card will be a heart, the second card will be a red card, and the third card will be a queen, we need to consider the probabilities of these events happening independently since the cards are drawn with replacement.

The probability of drawing a heart as the first card (P(Heart)) is calculated by dividing the number of hearts in the deck by the total number of cards:

• P(Heart) = number of hearts / total number of cards = 13/52 = 1/4

The probability of drawing a red card as the second card (P(Red)) includes both hearts and diamonds:

• P(Red) = (number of hearts + number of diamonds) / total number of cards = (13 + 13) / 52 = 1/2

The probability of drawing a queen as the third card (P(Queen)) is:

• P(Queen) = number of queens / total number of cards = 4/52 = 1/13

Since each draw is independent and with replacement, the probabilities are multiplied to find the combined probability:

Combined probability = P(Heart) x P(Red) x P(Queen) = 1/4 x 1/2 x 1/13 = 1/104

Thus, the probability of drawing a heart, then a red card, and then a queen in that order with replacement is 1/104.