Math Problem Statement

A group of people were asked if they had run a red light in the last year. 266 responded "yes", and 236 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 can use the following formula for probability:

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

  1. The number of people who responded "yes" is 266.
  2. The number of people who responded "no" is 236.
  3. Therefore, the total number of responses is:

266+236=502266 + 236 = 502

Now, we calculate the probability:

P(run red light)=2665020.530P(\text{run red light}) = \frac{266}{502} \approx 0.530

So, the probability is approximately 0.5300.530, or as a fraction, it remains 266502\frac{266}{502}, which simplifies to 133251\frac{133}{251}.

Let me know if you’d like a more detailed explanation or if you have any questions.


  1. What is the probability that a randomly chosen person has not run a red light?
  2. How can this probability be represented as a percentage?
  3. What would the probability be if the total number of people surveyed changed?
  4. How would the probability change if more people answered "yes"?
  5. What is the complement of this probability?

Tip: Probabilities are often represented as decimals, fractions, or percentages. Practice converting between these forms to become comfortable interpreting probability results.

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Math Problem Analysis

Mathematical Concepts

Probability
Fractions
Decimal Representation

Formulas

P(run red light) = number of 'yes' responses / total number of responses

Theorems

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Suitable Grade Level

Grades 6-8