I am supposed to solve the following problem:
The bus arrives at the stop every 4 minutes and the train, which stops right next to the bus, every 6 minutes. What is the probability that a bus will come before the train? What is the probability of a bus or train coming in two minutes?
My attempt:
Sample space will represents all the stops of the train and bus for one hour: 15*10=150. But I do not know how to represent the probability of the events.
Can anyone help me?
Best Answer
It's not well formulated, but usually they mean that $X \sim U(0,4)$ and $Y\sim U(0,6)$, where X denotes the bus arrival time and Y the train arrival time. Your space is the rectangle $(0,4)\times(0,6)$. Bus comes before the train is the event $X<Y$, bus and train come within 2 minutes is $|X-Y|<2$. The probability of these is their area divided by the are of the full rectangle.
Edit: as Ben W pointed out the second event might be $\min(X,Y)<2$.