Math Problem Statement

A group of people were asked if they had run a red light in the last year. 243 responded "yes", and 224 responded "no".

Find the probability that if a person is chosen at random, they have run a red light in the last year.

Give your answer as a fraction or decimal accurate to at least 3 decimal places

Solution

To find the probability that a randomly chosen person has run a red light in the last year, we use the formula for probability:

P(run red light)=number of "yes" responsestotal number of responsesP(\text{run red light}) = \frac{\text{number of "yes" responses}}{\text{total number of responses}}

Given:

  • Number of "yes" responses = 243
  • Number of "no" responses = 224
  • Total number of responses = 243 + 224 = 467

Now, the probability is:

P(run red light)=2434670.520P(\text{run red light}) = \frac{243}{467} \approx 0.520

So, the probability that a randomly chosen person has run a red light in the last year is approximately 0.5200.520 or 243467\frac{243}{467}.

Would you like more details or have any questions?

Here are 5 related questions:

  1. What is the probability that a randomly chosen person has not run a red light in the last year?
  2. How would the probability change if 50 more people responded "yes"?
  3. If another survey was conducted with double the number of respondents, how might the results differ?
  4. How can probabilities be used to predict future survey outcomes?
  5. What is the probability if 75% of the people had run a red light?

Tip: Probabilities are always between 0 and 1, where 1 means the event is certain to happen, and 0 means it is impossible.

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Math Problem Analysis

Mathematical Concepts

Probability
Basic Fractions
Ratio

Formulas

P(event) = number of favorable outcomes / total outcomes

Theorems

Basic Probability Theorem

Suitable Grade Level

Grades 6-8