Probability

Question

During the rush period at a certain train station, every 15 minutes an express train arrives and waites 4 minutes to pick up passengers. Four minutes after the express train leaves, a local train arrives at the station at a random time during the rush period, find the probability pf each of the following. 

 

a.) The express train will be waiting at the station

b.) No train will be waiting at the station

Answer 1

During the "rush period" you have units of 15 minutes (the amount of time between 1 express train and the next).  During each 15 minutes period, an express train will be sitting and waiting for 4 minutes.  So the probability that the express train will be waiting is 4/15. 

 

However, you don't tell how long the local train spends waiting at the station, so you can't figure the probability that no train will be waiting.  If it waits for 4 minutes also, that means there are 8 minutes out of ever 15 when there is a train waiting, so the probability that no train would be waiting is 7/15 (7 being 15-8).  If the local train only waits for 1 minute, then it would be 5/15.