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

0.14
0.14

0.43
0.43

0.34
0.34

0.22

Answer 1

To find \( P(A \text{ and } B) \), we need to determine the probability of both events occurring: being on time (Event A) and using a bus (Event B).

From the table, we see the following relevant information:

• The number of on-time bus arrivals is 46.
• The total number of events (total arrivals) is 320.

We calculate \( P(A \text{ and } B) \) as follows: \[ P(A \text{ and } B) = \frac{\text{Number of on-time bus arrivals}}{\text{Total number of arrivals}} = \frac{46}{320} \]

Now, we compute the probability: \[ P(A \text{ and } B) = \frac{46}{320} = 0.14375 \]

Rounding this to the nearest hundredth gives us: \[ P(A \text{ and } B) \approx 0.14 \]

Thus, the correct answer is 0.14.