A card is drawn from 52 cards. What is the probability that the second card is a face card? I hope the question is clear.
I believe the answer to be as follows…
Two cases –
Case 1: First card drawn is a face card.
Case 2: First card drawn is not a face card.
Then the total probability is $\;\frac{12\cdot 11}{52\cdot 51} + \frac{40\cdot 12}{52\cdot 51}$.
Best Answer
Your calculation is correct. However, note that the result simplifies to $(12\cdot11+40\cdot12)/(52\cdot51)=(11+40)\cdot12/(52\cdot51)=12/52$.
This is because you can just as well ignore the first card and argue that the probability of the second card being a face card is the number of face cards, $12$, divided by the total number of cards, $52$.