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

1351
Start Fraction 13 over 51 End Fraction

25102
Start Fraction 25 over 102 End Fraction

101102

Answer 1

To find the probability that both cards selected are black when drawing two cards without replacement from a standard deck of 52 cards, we can follow these steps:

1. **Calculate the probability of drawing the first black card:**
- There are 26 black cards in the 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. **Calculate the probability of drawing the second black card after the first black card has been drawn:**
- If the first card drawn was black, there are now 25 black cards remaining and 51 cards total left in the deck.
- So, the probability of drawing a second black card is:
\[
P(\text{2nd black | 1st black}) = \frac{25}{51}
\]

3. **Calculate the combined probability of both events:**
- The total probability of both cards being black is the product of the individual probabilities:
\[
P(\text{both black}) = P(\text{1st black}) \times P(\text{2nd black | 1st black}) = \frac{26}{52} \times \frac{25}{51} = \frac{1}{2} \times \frac{25}{51} = \frac{25}{102}
\]

Therefore, the probability that both cards are black is:
\[
\frac{25}{102}
\]

So the correct response is:
\[
\text{Start Fraction 25 over 102 End Fraction}
\]