Math Problem Statement

A group of people were asked if they had run a red light in the last year. The number of people that responded yes is 388 and no is 285. Find the probability that if a person is chosen at random, he/she has run a red light in the last year. Round to two decimal places.

Solution

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

P(A)=Number of favorable outcomesTotal number of outcomesP(A) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}

In this context:

  • The number of people who responded "yes" (favorable outcomes) is 388.
  • The number of people who responded "no" is 285.

First, calculate the total number of people surveyed:

Total number of people=Number of yes responses+Number of no responses\text{Total number of people} = \text{Number of yes responses} + \text{Number of no responses} Total number of people=388+285=673\text{Total number of people} = 388 + 285 = 673

Now, calculate the probability:

P(run a red light)=388673P(\text{run a red light}) = \frac{388}{673}

To express this probability as a decimal rounded to two decimal places, perform the division:

P(run a red light)3886730.576P(\text{run a red light}) \approx \frac{388}{673} \approx 0.576

Thus, the probability that a randomly chosen person has run a red light in the last year is approximately 0.580.58 (rounded to two decimal places).

Would you like details or have any questions? Here are five more questions you can ask:

  1. What is the probability that a randomly chosen person has not run a red light in the last year?
  2. How do you calculate the probability of multiple independent events?
  3. What are some common uses of probability in real life?
  4. Can you explain the concept of conditional probability?
  5. How does the law of large numbers relate to probability?

Tip: When working with probabilities, always ensure the sum of the probabilities of all possible outcomes equals 1. This helps verify the accuracy of your calculations.

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Math Problem Analysis

Mathematical Concepts

Probability

Formulas

Probability formula: P(A) = Number of favorable outcomes / Total number of outcomes

Theorems

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Suitable Grade Level

Grades 9-12