Steve and Cathy are playing a card game with a standard deck of $52$ playing cards. Cathy is dealt an ace and a four. Steve is dealt a jack.

1. How many cards are left in the deck?

   Hint (a):

   There were $52$ cards to begin with and 3 have been dealt. How many are left?

2. How many of the remaining cards are aces?

   Hint (b):

   In a standard deck, there are $4$ aces. One of them has been dealt.

3. If Steve gets an ace, he will win. What is the probability that he will get an ace on the next card he is dealt?

   Hint (c):

   Make the number of aces left the numerator and the number of cards left the denominator.

   Answer (c):

   $\frac{3}{49}$

4. Next Steve gets a two and Cathy gets a five. What is the probability that Steve will get a nine on the next card he is dealt?

   Hint (d):

   How many cards are left in the deck? How many of them are nines?

   Answer (d):

   $\frac{4}{47}$