Texted While Driving
714 Drove When Drinking​ Alcohol
3051
No Texting While Driving
177 Drove When Drinking​ Alcohol
4305
If four different high school drivers are randomly​ selected, find the probability that they all drove when drinking alcohol.

To find the probability that four randomly selected high school drivers all drove when drinking alcohol, we need to first calculate the overall probability that any one driver drove when drinking alcohol.

From the data provided:

- **Texted While Driving and Drove When Drinking Alcohol**: 714 students
- **No Texting While Driving but Drove When Drinking Alcohol**: 177 students

So, the total number of students who drove when drinking alcohol is:
\[
714 + 177 = 891
\]

Next, we need the total number of students surveyed:

- **Texted While Driving**: 3051 students
- **No Texting While Driving**: 4305 students

Thus, the total number of students surveyed is:
\[
3051 + 4305 = 7356
\]

### Step 1: Calculate the probability that one student drove when drinking alcohol
The probability that a randomly selected student drove when drinking alcohol is:
\[
P(\text{Drove when drinking alcohol}) = \frac{891}{7356}
\]

### Step 2: Find the probability that all four selected drivers drove when drinking alcohol
Since the selections are independent, the probability that all four drivers drove when drinking alcohol is the product of the probabilities for each driver:
\[
P(\text{All four}) = \left( \frac{891}{7356} \right)^4
\]

Let's compute this value.The probability that all four randomly selected high school drivers drove when drinking alcohol is approximately \( 0.000215 \), or 0.0215%.

Do you need further clarification or details?

Here are 5 related questions you might be interested in:
1. What is the probability that none of the four drivers drove when drinking alcohol?
2. How does the probability change if only two drivers are randomly selected?
3. What is the probability that exactly two out of four drivers drove when drinking alcohol?
4. How does the sample size affect the probability in similar problems?
5. How can we model this scenario with a binomial distribution?

**Tip:** Probabilities of independent events are multiplied when determining the likelihood of all events occurring together.

If four different high school drivers are randomly selected, find the probability that they all drove when drinking alcohol.

Find the probability that four randomly selected high school drivers all drove when drinking alcohol. This problem explores probability concepts and the multiplication rule of independent events, with a step-by-step solution suitable for high school students (Grades 9-12).

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