Use the table to answer the question.

Question

Arrival Time
Transport Type On Time Late TOTAL
Car 164 48 212
Bus 46 62 108
TOTAL 210 110 320
Let event A represent an on-time arrival and event B represent transportation by bus. What is P(A and B)? Round your answer to the nearest hundredth.

(1 point)
Responses

0.43
0.43

0.14
0.14

0.22
0.22

0.34

Answer 1

To find \( P(A \text{ and } B) \), we need to determine the number of people who arrived on time and used the bus, and then divide that by the total number of people.

From the table:

• The number of people who took the bus and were on time is 46.
• The total number of people is 320.

Now we can calculate \( P(A \text{ and } B) \):

\[ P(A \text{ and } B) = \frac{\text{Number of people who arrived on time and took the bus}}{\text{Total number of people}} = \frac{46}{320} \]

Calculating this fraction:

\[ P(A \text{ and } B) = \frac{46}{320} = 0.14375 \]

Rounding to the nearest hundredth gives us:

\[ P(A \text{ and } B) \approx 0.14 \]

Thus, the answer is:

0.14