2 leaves are randomly extracted from a pack of 52 leaves without replacement. By what probability (probability) can you say that both leaves are black?

Correct option is C

Step 1: Total number of ways to choose 2 cards.

The total number of ways to choose 2 cards from a deck of 52 cards is given by:
$$\binom{52}{2} = \frac{52 \times 51}{2} = 1326$$​

Step 2: Total number of ways to choose 2 black cards.
The total number of ways to choose 2 black cards from 26 black cards is:
$$\binom{26}{2} = \frac{26 \times 25}{2} = 325$$​

Step 3: Probability formula.
The probability of choosing 2 black cards is given by:
$$P(\text{both black}) = \frac{\text{Number of ways to choose 2 black cards}}{\text{Total number of ways to choose 2 cards}}$$​
Substitute the values:
$$P(\text{both black}) = \frac{325}{1326}$$​

Step 4: Simplify the fraction.
Simplify $$\frac{325}{1326}$$​ :
$$P(\text{both black}) = \frac{25}{102}$$​

Final Answer:

The probability that both cards are black is:
$$\frac{25}{102}$$​