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?

Answer 1

Since the first card selected is not returned, there are now 51 cards remaining in the deck, with 25 black cards and 26 red cards.

The probability of selecting a black card for the first draw is 26/52 = 1/2.

After selecting one black card, there are 25 black cards left in the deck and 50 total cards remaining.

The probability of selecting a black card for the second draw is 25/50 = 1/2.

Therefore, the probability of selecting two black cards in a row is:

(1/2) * (1/2) = 1/4

So, the probability that both cards are black is 1/4.