Elena’s bus runs every 20 minutes. If she arrives at her bus stop at a random time, what is the probability that she will have to wait at least 5 minutes for the bus if it is running on schedule?

Question

anonymous · Answer

Let's say that the bus comes at 12:00, 12:20, 12:40, 1:00, 1:20, etc.

Let's target the span of time between the first and second bus arriving (12:01-12:20). We can do this for any time, because in any span of 20 minutes, it's guaranteed a bus comes.

So let's say you get to the bus stop between 12:01 and 12:20, at what times would you have to wait at least 5 minutes for the bus at 12:20 to come?

johnweldon1993 · Answer

Right! As it was said above...there is a 20 minute span

If she arrives at 12:01 she must wait 19 minutes.
Arrives at 12:02 she must wait 18 minutes etc...

Now if she arrives at 12:15, she would have to wait 5 minutes for the bus to arrive.

So if she arrives at anytime between 12:01 and 12:15 (which is a 15 minute span out of the possible 20) she will have to wait AT LEAST 5 minutes as the question asks...

So the probability will be

$$\large \frac{15}{20}$$

This can be simplified more...