Question

Two cards are drawn at random and without replacement from a pack of 52 playing cards. Find the probability that both the cards are black.

Hint:

When calculating probabilities for successive events without replacement, multiply the probabilities of each event.

Answer 1

Step 1: Total number of cards.
A deck of 52 playing cards consists of 26 black cards (13 spades and 13 clubs) and 26 red cards.

Step 2: Probability of drawing the first black card.
The probability of drawing a black card from the deck is:
P(First black card) = 26 / 52 = 1 / 2

Step 3: Probability of drawing the second black card.
After drawing one black card, there are 25 black cards left and 51 cards remaining in the deck. The probability of drawing a black card now is:
P(Second black card) = 25 / 51

Step 4: Combined probability.
The probability that both cards drawn are black is the product of the two probabilities:
P(Both black cards) = 26 / 52 × 25 / 51 = 650 / 2652 = 25 / 102