To find \( P(A \text{ and } B) \), which is the probability that a train is both on time and a city-to-city train, we need to look for the intersection of the two events:
- Event A (On Time): 81 trains are on time (54 in the city + 27 city to city)
- Event B (City to City): 30 trains are city to city (27 on time + 3 late)
From the table, we see that:
- The number of city-to-city trains that are on time is 27.
The total number of trains is 90. Therefore, the probability \( P(A \text{ and } B) \) is calculated as:
\[ P(A \text{ and } B) = \frac{\text{Number of city to city trains that are on time}}{\text{Total number of trains}} = \frac{27}{90} \]
Now, simplifying:
\[ P(A \text{ and } B) = \frac{27}{90} = \frac{3}{10} = 0.3 \]
Thus,
\[ P(A \text{ and } B) = 0.3 \]
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