Math Problem Statement

IN a room of 50 people How many people in the room live at a property where the last digit of their street number is equal to 7?

Solution

To determine how many people in a room of 50 live at a property where the last digit of their street number is equal to 7, we can assume that the street numbers are randomly and uniformly distributed across all possible last digits (0 through 9).

Since there are 10 possible last digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9), the probability that any person's street number ends in 7 is 1 out of 10.

Thus, the expected number of people living at a property where the last digit of the street number is 7 can be calculated as:

Expected number=110×50=5\text{Expected number} = \frac{1}{10} \times 50 = 5

So, we expect that 5 people in the room live at a property where the last digit of their street number is 7.

Would you like any further details or clarification on this?

Here are 5 related questions to expand on this:

  1. What is the probability that no one in the room lives at a property with a street number ending in 7?
  2. How would the expected number change if there were 100 people in the room?
  3. What is the likelihood that more than 10 people have a street number ending in 7?
  4. How would the analysis change if some people shared the same address?
  5. What is the probability that exactly 5 people live at a property where the street number ends in 7?

Tip: The concept of probability distribution assumes random and uniform distribution unless specified otherwise.

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Math Problem Analysis

Mathematical Concepts

Probability
Uniform Distribution
Expected Value

Formulas

P(last digit = 7) = 1/10
Expected number = P(last digit = 7) * total people

Theorems

Law of Large Numbers

Suitable Grade Level

Grades 8-10