Question

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)
O 0.43
• 0.14
0 0.34
• 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 (event A) and transportation by bus (event B).

First, let's identify the number of on-time arrivals using a bus from the table provided:

- Total number of on-time arrivals by bus = 46

Next, we need to determine the total number of events (total number of transports):

- Total transports = 320

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

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

Now let's calculate the fraction:

\[
\frac{46}{320} = 0.14375
\]

When rounding to the nearest hundredth:

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

Therefore, the answer is:

**0.14**