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.

Question

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:

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