Dharen has to randomly select two cards from a standard deck of 52 cards without returning the first card. A standard deck of cards has 26 black cards and 26 red cards. What is the probability that both cards are black?(1 point) Responses 1351 Start Fraction 13 over 51 End Fraction 101102 Start Fraction 101 over 102 End Fraction 25102 Start Fraction 25 over 102 End Fraction 25104 Start Fraction 25 over 104 End Fraction
To find the probability that both cards are black, we start by looking at the total number of possible outcomes when selecting two cards from a standard deck without replacement.
The total number of ways to choose the first card is 52 (since there are 52 cards in the deck). Once the first card is chosen, there are 51 cards remaining in the deck. Therefore, the total number of ways to choose the second card is 51.
To find the number of ways to choose two black cards, we first calculate the number of ways to choose the first black card, which is 26 (since there are 26 black cards in the deck). Once the first black card is chosen, there are 25 black cards and 51 total cards remaining. Therefore, the number of ways to choose the second black card is 25.
The probability of both cards being black is the number of ways to choose two black cards divided by the total number of ways to choose two cards:
(26/52) * (25/51) = 650 / 2652 = 25 / 102
Therefore, the probability that both cards are black is 25/102. So, the answer is 25/102.