Respuesta :
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:
[tex] P(\text{news are on}) = \cfrac{13}{60} [/tex]
[tex] P(\text{commercials are on}) = \cfrac{2}{60} = \cfrac{1}{30} [/tex]
[tex] P(\text{music is on}) = \cfrac{45}{60} = \cfrac{3}{4} [/tex]
