Lenny’s favorite radio station has this schedule : news: 13min commercials: 2 min. music: 45min. if lenny chooses a time of day at random to turn on the radio to his favorite station, what is the probability that the news will be on?

Let's focus on a single hour. Once you know the probability of a certain hour, all hour will have the same time schedule, and so the probability will be the same.

Since a hour is composed by 60 minutes, the 13 minutes of news compose the 13/60 of the given time. For the sake of completeness, news compose the 2/60 of the given time, and music the 45/60 of the given time.

Again, this is the way a single hour is scheduled. Since Lenny will choose a random time of the day, we will turn the radio on during a particular hour, which will be structured as we just described.

So, let's say that that Lenny will turn the radio on between 3 and 4 pm (these numbers are just for example purpose, since every hour will work in the same way). During this hour, the news are up 13/60 of the time.

So, this is the probability that the news will be on. The complete schema is the following: