You can win concert tickets from a radio station if you are the first person to call when the song of the day is played, or if you are the first person to correctly answer the trivia question. the song of the day is announced at a random time between 7: 00 and 7: 30

a. m. the trivia question is asked at a random time between 7: 15 and 7: 45

a. m. you begin listening to the radio station at 7: 20. find the probability that you miss the announcement of the song of the day or the trivia question. express your answer as a fraction in simplest form.

The song of the day is announced at a random time between 7:00 and 7:30, so you have a 30-minutes span of time where the song could be announced. If you start listening to the radio 20 minutes in, you're at 2/3 of the time. So, there is a 2/3 chance that the song has already been chosen, and a 1/3 chance that it will be announced in the remaining 10 minutes.

Similarly, the trivia question is asked at a random time between 7:15 and 7:45 so there is again a 30-minutes span of time. But this time, we're only 5 minutes late, so there is a 5/30=1/6 chance that the question was already asked, and a 25/30=5/6 chance that the question will be asked in the remaining 25 minutes.

So, there are four scenarios:

You're interested in the probability of missing either of the announcements, so you want to sum the two middle cases (in the first you miss everything, in the second you don't miss anything).

Your result is thus

50

step-by-step explanation:

you can first factor out the n to get n(1+5). we know that 1+5 is 6, so we just have 6n.