Lenny’s favorite radio station has this schedule:
news: 15 min.
commercials: 3 min.
music: 42 min.
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?
total time = 60
prob (news) = 15/60 = 1/4
To find the probability that the news will be on when Lenny turns on the radio, we first need to calculate the total duration of each type of content on the radio station.
The total duration of one cycle on Lenny's favorite radio station is the sum of the durations of the news, commercials, and music:
Total duration = news duration + commercials duration + music duration
Total duration = 15 min + 3 min + 42 min
Total duration = 60 min
Now, we can calculate the probability of the news being on when Lenny turns on the radio. Since Lenny chooses a time at random, all moments within a cycle have an equal chance of being selected. Therefore, the probability is the duration of the news divided by the total duration:
Probability of news = news duration / total duration
Probability of news = 15 min / 60 min
Probability of news = 1/4 or 0.25 (25%)
So, the probability that the news will be on when Lenny turns on the radio is 25%.
To determine the probability of the news being on, we need to calculate the proportion of the schedule that is dedicated to news.
The total duration of a schedule is given by the sum of the durations of each segment:
Total duration = news duration + commercials duration + music duration
Total duration = 15 min + 3 min + 42 min = 60 min
Now, we can calculate the probability of the news being on:
Probability of news = news duration / total duration
Probability of news = 15 min / 60 min
Probability of news = 1/4
Therefore, the probability that the news will be on when Lenny randomly turns on the radio is 1/4 or 25%.