# Probability of picking the only two same cards out of 25 cards if I can only pick twice

In a set of 25 cards where two cards are only the same, what is the probability of picking those two same cards if I can only pick twice?

What I only know is that at first pick it is 2/25 equivalent to 8% chance. For the second pick it would be 1/24 (only if the first pick was a success) which is equivalent to 4.17% chance.

How can I compute for the probability having these results? I'm just asking this out of curiosity. Thanks a lot.

Your first steps are correct. Let $$A$$ be the event in which we pick one of the two cards in the first turn, and $$B$$ the event in which we pick the other card in the second turn. Using the definition of conditional probability, we have:
$$P(A, B) = P(A) P(B | A) = \frac{2}{25} \frac{1}{24} = \frac{1}{300}$$
$$P(A, B) = \frac{1}{25 \choose 2} = \frac{1}{\frac{25!}{23!2!}} = \frac{1}{\frac{25 \cdot 24}{2}} = \frac{1}{300}$$