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
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%.
To determine the probability that both cards selected are black, we need to find the probability of selecting a black card on the first draw and then multiply it by the probability of selecting another black card on the second draw.
Step 1: Calculate the probability of selecting a black card on the first draw:
There are 26 black cards out of the total 52 cards in the deck, so the probability of selecting a black card on the first draw is 26/52 or 1/2.
Step 2: Calculate the probability of selecting a black card on the second draw after removing one black card:
After the first black card is removed, there are 25 black cards remaining in the deck. The total number of cards remaining is now 51. So, the probability of selecting a black card on the second draw is 25/51.
Step 3: Multiply the probabilities from Steps 1 and 2:
To find the probability of both events occurring, we multiply the probabilities together:
(1/2) * (25/51) = 25/102.
Therefore, the probability that both cards selected are black is 25/102.