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.

Question

A. 0.22
B. 0.34
C. 0.43
D. 0.14

Answer 1

To find \( P(A \text{ and } B) \), which is the probability of an on-time arrival (event A) and transportation by bus (event B), we can use the data provided.

1. Total number of participants: 320 (from the totals)
2. Number of on-time arrivals using the bus: 46 (from the table under "Bus" and "On Time")

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

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

Now let's compute the fraction:

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

Rounding this to the nearest hundredth gives us:

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

Thus, the answer is:

D. 0.14