Question

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 0.14 0.14 0.43 0.43 0.22 0.22 0.34

Answer 1

To find \( P(A \text{ and } B) \), we need to determine the probability of an event where a person arrives on time (event A) and uses a bus (event B).

From the table, we can see:
- The number of on-time arrivals by bus is 46.
- The total number of arrivals (both on time and late) is 320.

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

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

Calculating the above fraction:

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

Rounding this to the nearest hundredth:

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

Thus, the answer is \( \boxed{0.14} \).