Question

Daren randomly selected two cards froma standard deck of 52 cards without returning the first card. A standard deck of cards has 26 black arms and 26 red cards. What is the probability that both cards are black

Answer 1

There are 26 black cards out of 52 cards total, so the probability of selecting a black card on the first draw is 26/52 = 1/2. Since Daren did not return the first card, there are now 51 cards left in the deck, with 25 black cards remaining. Therefore, the probability of selecting a black card on the second draw, given that the first card was black and was not returned, is 25/51.

To find the probability of both events happening together, we multiply the probabilities:

P(both cards are black) = P(first card is black) x P(second card is black given that the first card was black)

P(both cards are black) = (1/2) x (25/51)

P(both cards are black) ≈ 0.2451 or about 24.51%

Therefore, the probability that Daren randomly selected two black cards from a standard deck of cards without returning the first card is approximately 0.2451 or about 24.51%.