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

0.34
0.34

0.43
0.43

0.14
0.14

0.22

Answer 1

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

From the table:

• The number of on-time arrivals by bus (which corresponds to event A and B both happening) is 46.
• The total number of arrivals is 320.

The probability \( P(A \text{ and } B) \) is calculated as:

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

Calculating this value:

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

Rounding to the nearest hundredth:

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

Thus, the answer is 0.14.