On a recent Saturday, a total of 1252 people visited a local library. Of these people, 257 were under age 10, 453 were aged 10-18, 160 were aged 19-30, and the rest were more than 30 years old. One person is sampled at random.

Question

(a) What is the probability that the person is less than 10years old?

(b) What is the probability that the person is more than 10 years old?

Answer 1

To find the requested probabilities, we need to use the total number of people who visited the library and the number of people in each age group.

Total number of visitors: \[ 1252 \]

Given data:

• Under age 10: \[ 257 \]
• Aged 10-18: \[ 453 \]
• Aged 19-30: \[ 160 \]

First, let's calculate the number of people who are more than 30 years old.

\[ \text{Total under 10, 10-18, and 19-30} = 257 + 453 + 160 = 870 \]

Now, we can find the number of people more than 30 years old:

\[ \text{People more than 30} = 1252 - 870 = 382 \]

Now we can calculate the probabilities.

(a) The probability that a randomly selected person is less than 10 years old can be calculated as:

\[ P(\text{less than 10 years old}) = \frac{\text{Number of people under 10}}{\text{Total number of visitors}} = \frac{257}{1252} \]

So, we calculate:

\[ P(\text{less than 10 years old}) = \frac{257}{1252} \approx 0.205 \]

(b) The probability that a randomly selected person is more than 10 years old can be calculated as:

\[ P(\text{more than 10 years old}) = \frac{\text{Number of people more than 10}}{\text{Total number of visitors}} = \frac{1252 - 257}{1252} = \frac{995}{1252} \]

So, we calculate:

\[ P(\text{more than 10 years old}) = \frac{995}{1252} \approx 0.795 \]

In summary:

• (a) \( P(\text{less than 10 years old}) \approx 0.205 \)
• (b) \( P(\text{more than 10 years old}) \approx 0.795 \)