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.

Question

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

$$\boxed{{\displaystyle 0.5889}}$$