Question

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

25104
Start Fraction 25 over 104 End Fraction

101102
Start Fraction 101 over 102 End Fraction

1351
Start Fraction 13 over 51 End Fraction

25102

Answer 1

To find the probability that both cards drawn from a standard deck of 52 cards are black, we can break it down into steps:

1. **Probability of drawing the first black card**: There are 26 black cards in a deck of 52 cards. So the probability of drawing the first black card is:
\[
P(\text{1st black}) = \frac{26}{52} = \frac{1}{2}
\]

2. **Probability of drawing the second black card**: After drawing the first black card, there are now 25 black cards remaining in a deck of 51 cards. So the probability of drawing the second black card is:
\[
P(\text{2nd black} | \text{1st black}) = \frac{25}{51}
\]

3. **Combined probability**: The probability that both cards drawn are black is the product of the probabilities of each event:
\[
P(\text{both black}) = P(\text{1st black}) \times P(\text{2nd black} | \text{1st black}) = \frac{26}{52} \times \frac{25}{51} = \frac{1}{2} \times \frac{25}{51} = \frac{25}{102}
\]

Thus, the probability that both cards are black is \( \frac{25}{102} \).

The correct option is:
- \( \frac{25}{102} \)