A group of people were asked if they had run a red light in the last year. 388 responded "yes", and 322 responded "no".

Find the probability that if a person is chosen at random,

(a) the person ran a red light.

Express your answer as a reduced fraction.

(b) the person did not run a red light.

Express your answer as a reduced fraction

To solve this, we can use basic probability formulas. The probability of an event is given by the ratio of favorable outcomes to the total number of outcomes.

Let’s first find the total number of people surveyed:

\[
\text{Total people} = 388 \, (\text{yes}) + 322 \, (\text{no}) = 710
\]

### (a) Probability that the person ran a red light:
The number of people who ran a red light is 388. Therefore, the probability \( P(\text{ran red light}) \) is:

\[
P(\text{ran red light}) = \frac{388}{710}
\]

To reduce the fraction, we find the greatest common divisor (GCD) of 388 and 710, which is 2. So we divide both the numerator and the denominator by 2:

\[
P(\text{ran red light}) = \frac{388 \div 2}{710 \div 2} = \frac{194}{355}
\]

So, the probability is:

\[
P(\text{ran red light}) = \frac{194}{355}
\]

### (b) Probability that the person did not run a red light:
The number of people who did not run a red light is 322. Therefore, the probability \( P(\text{did not run red light}) \) is:

\[
P(\text{did not run red light}) = \frac{322}{710}
\]

Similarly, we reduce this fraction by finding the GCD of 322 and 710, which is 2. So:

\[
P(\text{did not run red light}) = \frac{322 \div 2}{710 \div 2} = \frac{161}{355}
\]

Thus, the probability is:

\[
P(\text{did not run red light}) = \frac{161}{355}
\]

### Final Answers:
- (a) Probability that the person ran a red light: \( \frac{194}{355} \)
- (b) Probability that the person did not run a red light: \( \frac{161}{355} \)

Would you like more details or have any questions? 

Here are 5 related questions you might find interesting:
1. What is the probability of selecting two people who both ran a red light?
2. What is the probability of selecting a person who either ran or did not run a red light?
3. How does the probability change if 50 more people responded "no"?
4. What is the complement of the event that a person ran a red light?
5. How do we calculate the probability of independent events in a survey?

**Tip**: Always reduce fractions to their simplest form to ensure clear and precise probabilities.

A group of people were asked if they had run a red light in the last year. 388 responded 'yes', and 322 responded 'no'. Find the probability that if a person is chosen at random, (a) the person ran a red light. Express your answer as a reduced fraction. (b) the person did not run a red light. Express your answer as a reduced fraction.

Learn how to calculate the probability of a person running a red light, based on a survey where 388 people responded 'yes' and 322 responded 'no'. Includes a step-by-step breakdown of probability calculations, fraction reduction using GCD, and a simplified answer. Suitable for students in Grades 6-8.

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