Question

Train Arrival
train path in the city/On time arrival = 54/late arrival = 6/total is 60
city to city/on time arrival = 27/late arrival = 3/total is 30

Let event A be the train that is on time and event B be the city to city train. What is P (A and B)

Answer 1

To find the probability of both events A and B occurring (P(A and B)), we need to determine the number of outcomes where the train is both on time (event A) and a city-to-city train (event B).

From the information provided, we have the following:

- In the city trains:
- On time arrivals: 54
- Late arrivals: 6
- Total: 60

- In the city-to-city trains:
- On time arrivals: 27
- Late arrivals: 3
- Total: 30

Assuming that the city-to-city trains are distinct from the city trains, we can summarize the outcomes as follows:

- Total on time arrivals from city trains = 54
- Total on time arrivals from city-to-city trains = 27

Since we want the total number of on-time arrivals from city-to-city trains, we can directly see that event A (on time) and event B (city-to-city) both happening is represented by the on-time arrivals for city-to-city trains, which is 27.

Thus, the probability of both events A and B occurring is:

\[ P(A \text{ and } B) = \frac{\text{Number of city-to-city trains that are on time}}{\text{Total trains}} \]

Now calculate the total number of trains:

- Total trains from the city: 60
- Total trains from city-to-city: 30

Total number of trains = 60 + 30 = 90

Now, we can find the probability:

\[ P(A \text{ and } B) = \frac{27}{90} = \frac{3}{10} \]

So, the probability \( P(A \text{ and } B) = 0.3 \).