Step 1 :Construct a sample space, and find the probability that both bills have the same value. The probability that both bills have the same value is \(\frac{1}{3}\).
Step 2 :Next, find the probability that the second bill is larger than the first bill. Consider the possible combinations of bills that Ebony could pull out of her wallet. The possible combinations are (1,5), (1,10), (5,1), (5,10), (10,1), (10,5).
Step 3 :Out of these combinations, the ones where the second bill is larger than the first are (1,5), (1,10), and (5,10). So, the probability that the second bill is larger than the first is 3 out of 6, or \(\frac{1}{2}\).
Step 4 :Final Answer: The probability that the second bill is larger than the first bill is \(\boxed{\frac{1}{2}}\).