After a late night of studying, Ebony decides to grab a latte before class so she can stay awake through her morning lecture. She has only a one-dollar bill, a five-dollar bill, and a ten-dollar bill in her wallet. She pulls one out and looks at it, but then she puts it back. Distracted by a flyer for a new campus organization, she randomly hands a bill from her wallet to the clerk.
Construct a sample space, and find the probability that
(a) Both bills have the same value.
(b) The second bill is larger than the first bill.
(c) The value of each of the two bills is even.
(d) The value of exactly two of the bills is odd.
(e) The sum of the values of both bills is less than $\$ 10$.
Write your answers in exact, simplified form.
Part 1 of 5
(a) The probability that both bills have the same value is $\frac{1}{3}$.
Part: $1 / 5$
Part 2 of 5
(b) The probability that the second bill is larger than the first bill is
Answer
Final Answer: The probability that the second bill is larger than the first bill is \(\boxed{\frac{1}{2}}\).
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 \(\boxed{\frac{1}{2}}\).
