Use the table to answer the 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

1 answer

To find \( P(A \text{ and } B) \), we need to determine the probability of both events A (on-time arrival) and B (transportation by bus) occurring together.

From the table, we can find the number of bus arrivals that were on time. The data shows:

  • Number of on-time arrivals for the bus: 46

The total number of arrivals is 320.

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

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

Next, we perform the division:

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

Rounding to the nearest hundredth, we get:

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

Therefore, the answer is 0.14.