A book contains 92 pages. A page is chosen at random. What is the probability that the sum of the digits in the page number is 9?

Answer

To solve the problem of finding the probability that the sum of the digits in a randomly chosen page number from a book of 92 pages equals 9, we can follow these steps:

### Step 1: Identify the total number of pages
The book contains a total of 92 pages.

### Step 2: Determine the favorable outcomes
We need to find all the page numbers where the sum of the digits equals 9. We can list the page numbers and calculate the sum of their digits:

1. **Page 9**: 0 + 9 = 9
2. **Page 18**: 1 + 8 = 9
3. **Page 27**: 2 + 7 = 9
4. **Page 36**: 3 + 6 = 9
5. **Page 45**: 4 + 5 = 9
6. **Page 54**: 5 + 4 = 9
7. **Page 63**: 6 + 3 = 9
8. **Page 72**: 7 + 2 = 9
9. **Page 81**: 8 + 1 = 9
10. **Page 90**: 9 + 0 = 9

Thus, the favorable outcomes where the sum of the digits equals 9 are: 9, 18, 27, 36, 45, 54, 63, 72, 81, and 90. This gives us a total of **10 favorable outcomes**.

### Step 3: Calculate the probability
The probability \( P \) of an event is given by the formula:

\[ P = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]

In this case, the number of favorable outcomes is 10, and the total number of outcomes (total pages) is 92. Therefore, the probability is:

\[ P = \frac{10}{92} \]

### Step 4: Simplify the fraction
To simplify \( \frac{10}{92} \):

\[ P = \frac{10 \div 2}{92 \div 2} = \frac{5}{46} \]

### Final Answer
The probability that the sum of the digits in the page number is 9 is \( \frac{5}{46} \).

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