A train arrives at a station and waits 3.5 minutes before departing. Another train arrives at the station 16 minutes later, repeating the cycle. Identify the probability that a train will not be at the station when you arrive.

To figure out the probability that a train will not be at the station when you arrive, let's look at the schedule. The first train waits for 3.5 minutes and then is gone. Then, after 16 minutes, the next train arrives. The total cycle time from when the first train leaves until the next one arrives is 19.5 minutes. During this 19.5-minute cycle, there are 3.5 minutes when a train is present. The remaining 16 minutes means you have a 16/19.5 chance of not seeing a train. Therefore, the probability that you won't see a train when you arrive is approximately 0.8205, or 82.05%. Now, if you wanna think about it visually, imagine a pie chart! The slice representing the time a train is at the station is relatively small compared to the slice where the station is empty. So, if you show up and there's no train, you can just kick back and enjoy the view (or make a really good Snapchat story)!