Find the probability that a number selected at random from 41 to 56 is a multiple of 9

1. Analyze the Question

We need to find the probability of picking a multiple of 9 from the set of integers ranging from 41 to 56 (inclusive).

2. Explain the Concept

Probability is defined as:

• Total outcomes: The count of numbers from 41 to 56.
• Favorable outcomes: The count of numbers in that range that are divisible by 9.

3. Show the Solution

Step 1: Find the total number of outcomes. To find the number of integers in an inclusive range $[a, b]$, use the formula: $(b - a) + 1$.

Step 2: Identify the multiples of 9 within the range 41 to 56. Let's list the multiples of 9:

• $9 \times 4 = 36$ (Too small)
• $9 \times 5 = 45$ (Within range)
• $9 \times 6 = 54$ (Within range)
• $9 \times 7 = 63$ (Too large)

The multiples of 9 in the range are 45 and 54. There are 2 favorable outcomes.

Step 3: Calculate the probability.

Simplify the fraction by dividing both the numerator and the denominator by 2:

4. Identify the Answer

Comparing our result to the options provided, the correct choice is A.

5. Exam Tip

When counting numbers in an inclusive range (e.g., "from X to Y"), students often forget to add the "+1". Always remember: if you are counting from 1 to 3, there are 3 numbers (1, 2, 3). If you just did $3 - 1$, you would get 2, which is incorrect. Adding the 1 ensures you include both endpoints!