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

0.22
0.22

0.43
0.43

0.14
0.14

Answer 1

To find \( P(A \text{ and } B) \), we need to determine the probability that an arrival is both on-time (event A) and by bus (event B).

From the table:

• The number of on-time arrivals by bus is 46.
• The total number of arrivals is 320.

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

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

Now calculate the fraction:

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

Rounding to the nearest hundredth gives us:

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

So, the answer is \( 0.14 \).