Drawing two cards from 52, what is the probability that the second card has a higher face value than the first?
The probability that the second card has the same face as the first is \(\frac{4-1}{52-1}=\frac{3}{51}\) (since there are only four cards with the same face).
The probability that the second card will be different(lower or higher) from the first is \(\frac{51}{51}-\frac{3}{51}=\frac{48}{51}\).
The chance than the card will be higher is the same as the card will be lower.
So that,the probability that the second card has a higher face value than the first is \(\frac{\frac{48}{51}}{2}=\frac{24}{51}\)