Question

For a class assignment, Alan wanted to study whether or not the color of a person's car correlates with the color of his or her hair. He spent an hour at a stoplight recording the color of each car that passed and the hair color of its driver.
Light car Dark car
Light hair 2 8
Dark hair 5 4
What is the probability that a randomly selected driver has dark hair and has a light car?
Simplify any fractions.

Answer 1

To find the probability that a randomly selected driver has dark hair and drives a light car, we can use the data provided in the table.

Here’s the data summarized:

- **Light hair with Light car:** 2
- **Light hair with Dark car:** 8
- **Dark hair with Light car:** 5
- **Dark hair with Dark car:** 4

Now, we first need to determine the total number of drivers recorded:

\[
\text{Total} = (2 + 8) + (5 + 4) = 2 + 8 + 5 + 4 = 19
\]

Next, the number of drivers with dark hair who also drive a light car is 5.

Now, we can find the probability of the event by using the formula:

\[
P(\text{Dark hair and Light car}) = \frac{\text{Number of dark hair drivers with light cars}}{\text{Total number of drivers}}
\]

Plugging in the values, we get:

\[
P(\text{Dark hair and Light car}) = \frac{5}{19}
\]

Thus, the probability that a randomly selected driver has dark hair and drives a light car is:

\[
\frac{5}{19}
\]