If it is known that 4 cards have different suits, what is the probability that the first card is a face card? Without replacement.

Question

I'm assuming this is a conditional probability question. Because the four cards are of different suits, we have 52 choices for the first card. Then whatever the first card is, throw away the remaining cards of that suit. In a similar fashion, there are 39 choices for the second card, 26 for the third, and 13 for the fourth. Therefore, the answer should be:

$P(E) = \frac{13\cdot 39\cdot 26\cdot 13}{52\cdot 39\cdot 26\cdot 13} = \frac{3}{13}$

Is my logic correct?

Answer 1

Yes, your logic and the answer you arrive at are correct.