A wallet containing 2 five-dollar bills, 9 ten-dollar bills, and 5 twenty-dollar bills is found and returned to its owner. The wallet's owner. The wallet's owner will reward the finder with 1 bill drawn randomly from the wallet. What is the probability that the bill drawn will be a twenty-dollar bill?

Options

A. `1/16`
B. `1/10`
C. `1/5`
D. `5/16`

Answer

To solve the problem of finding the probability that the bill drawn will be a twenty-dollar bill, we can follow these steps:

### Step 1: Identify the number of each type of bill
We have:
- 2 five-dollar bills
- 9 ten-dollar bills
- 5 twenty-dollar bills

### Step 2: Calculate the total number of bills
To find the total number of bills in the wallet, we add the number of each type of bill together:
\[ \text{Total bills} = \text{Number of } \$5 \text{ bills} + \text{Number of } \$10 \text{ bills} + \text{Number of } \$20 \text{ bills} \]
\[ \text{Total bills} = 2 + 9 + 5 = 16 \]

### Step 3: Identify the number of favorable outcomes
The number of favorable outcomes for drawing a twenty-dollar bill is simply the number of twenty-dollar bills in the wallet, which is:
\[ \text{Number of } \$20 \text{ bills} = 5 \]

### Step 4: Calculate the probability
The probability \( P \) of drawing a twenty-dollar bill is given by the ratio of the number of favorable outcomes to the total number of outcomes:
\[ P(\text{drawing a } \$20 \text{ bill}) = \frac{\text{Number of } \$20 \text{ bills}}{\text{Total bills}} = \frac{5}{16} \]

### Step 5: Simplify the probability (if necessary)
In this case, \( \frac{5}{16} \) is already in its simplest form.

### Final Answer
Thus, the probability that the bill drawn will be a twenty-dollar bill is:
\[ \frac{5}{16} \]

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