A bus arrives at bus station every 10 minutes and waits for 1.5 minutes. What is the probability that there will be a bus at the station when you arrive?

Question

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Answer 1

Here is the time line:

 

0     1     2     3     4     5     6     7     8     9     0     1     2     3     4  . . .

BB                                                                BB                           . . .

 

Probability is defined as (the number of successful events) / (the number of possible events).

 

For a continuous time, that means 1.5 minutes in ever 10 minute interval.  P = 1.5 / 10 = 0.15.

 

Now, this assumes that there is one bus, that arrivals are evenly spaced 10 minutes apart, and that your arrival is equally likely to be any time during a given 10-minute interval.  So, the question is better stated, "What is the probability that a bus will be at the station at any randomly-selected time?".