Question

What is the answer to the following question and how do you solve it? "Three cards are dealt from a shuffled standard deck of playing cards without replacement.Find the probability that the first card dealt is red, the second is black, and the third is red."

Answer 1

To find the probability that the first card dealt is red, the second card is black, and the third card is red, we can consider the number of red and black cards in the deck and calculate the probability for each draw.

Step-by-step explanation:

To find the probability that the first card dealt is red, the second card is black, and the third card is red, we can start by considering the number of cards in the deck. A standard deck of playing cards consists of 52 cards, with 26 red cards and 26 black cards.

Since the cards are dealt without replacement, the probability of drawing a red card on the first draw is 26/52. Once a red card is drawn, there are now 51 cards left in the deck, including 25 black cards. So the probability of drawing a black card on the second draw is 25/51. Finally, there are 50 cards remaining in the deck, including 25 red cards. So the probability of drawing a red card on the third draw is 25/50.

Now, we can calculate the overall probability by multiplying the individual probabilities together: (26/52) * (25/51) * (25/50) = 0.2451, or approximately 0.25. Therefore, the probability that the first card dealt is red, the second card is black, and the third card is red is approximately 0.25, or 25%.