Math Problem Statement

A group of people were asked whether they owned a dog. The number of people that owned a dog was 215, and 461 responded that they didn't own a dog. Find the probability that if a person is chosen at random, he/she own a dog. Round your answer to two decimal places.

Solution

To find the probability that a randomly chosen person owns a dog, we use the formula for probability:

P(owning a dog)=Number of people who own a dogTotal number of people surveyedP(\text{owning a dog}) = \frac{\text{Number of people who own a dog}}{\text{Total number of people surveyed}}

We are given:

  • Number of people who own a dog = 215
  • Number of people who don't own a dog = 461

So, the total number of people surveyed is:

Total number of people=215+461=676\text{Total number of people} = 215 + 461 = 676

Now, calculate the probability:

P(owning a dog)=2156760.318P(\text{owning a dog}) = \frac{215}{676} \approx 0.318

Rounded to two decimal places, the probability is:

P(owning a dog)=0.32P(\text{owning a dog}) = 0.32

Final Answer: 0.32

Would you like a more detailed explanation or have any questions about this?

Here are 5 related questions:

  1. What is the probability that a randomly chosen person does not own a dog?
  2. If 1000 people were surveyed, how many would you expect to own a dog?
  3. What would happen to the probability if the number of dog owners increased by 50?
  4. How would you calculate the odds of owning a dog instead of the probability?
  5. How does the probability change if some people did not respond to the survey?

Tip: Always verify that the total number of outcomes in probability includes all possible responses, such as both owning and not owning a dog in this case.

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Math Problem Analysis

Mathematical Concepts

Probability
Ratios
Basic Arithmetic

Formulas

P(event) = Number of favorable outcomes / Total number of outcomes

Theorems

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Suitable Grade Level

Grades 6-8