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 0.22 0.22 0.34 0.34 0.43 0.43 0.14

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 0.22 0.22 0.34 0.34 0.43 0.43 0.14

GPT-4o mini · Answer

To find $P(A \text{ and } B)$, we need to determine the probability that an arrival is on time (event A) and that the transport type is a bus (event B). From the table, we can identify the counts: - The total number of arrivals: 320 - The number of on-time arrivals by bus: 46 Now, we can calculate $P(A \text{ and } B)$: $$ P(A \text{ and } B) = \frac{\text{Number of on-time arrivals by bus}}{\text{Total number of arrivals}} = \frac{46}{320} $$ Calculating: $$ P(A \text{ and } B) = \frac{46}{320} = 0.14375 $$ Rounding to the nearest hundredth: $$ P(A \text{ and } B) \approx 0.14 $$ Thus, the answer is $ \boxed{0.14} $.