Question

A survey of 300 college students shows the average number of minutes that people talk on their cell phones each month. Round your answer to at least four decimal places.

Men:
Less than 600: 74
600-799: 13
800-999: 20
1000 or more: 19

Women
Less than 600: 65
600-799: 125
800-999: 9
1000 or more: 2
If a person is selected at random, find the probability that the person talked less than 600 minutes if it is known that the person was a man.

Answer 1

To find the probability that a randomly selected person talked less than 600 minutes given that they are a man, we can use the formula for conditional probability:

\[
P(A|B) = \frac{P(A \cap B)}{P(B)}
\]

Where:
- \( A \) is the event that a person talked less than 600 minutes.
- \( B \) is the event that the person is a man.

From the data given:
- The number of men surveyed is the sum of all the men, which is:

\[
74 + 13 + 20 + 19 = 126
\]

- Therefore, the total number of men, \( P(B) \), equals 126.

- The number of men who talked less than 600 minutes, \( P(A \cap B) \), is 74 (given).

Now, substituting these values into the formula:

\[
P(A|B) = \frac{74}{126}
\]

Calculating that:

\[
P(A|B) \approx \frac{74}{126} \approx 0.5889
\]

Thus, the probability that a randomly selected person talked less than 600 minutes given that they are a man is approximately

\[
0.5889
\]

So, rounding to four decimal places, the answer is

\[
\boxed{0.5889}
\]