1. Try to estimate the probability you\'d turn on the radio and hear a song you
ID: 3042466 • Letter: 1
Question
1. Try to estimate the probability you'd turn on the radio and hear a song you were thinking about. In other words, estimate the probability of the combined event P(thinking of a song)P(turn on the radio and hear the song) Take these factors into account: . The likelihood you'd hear the song during a randomly selected time of day (think about how frequently the song plays, at what times of day and on what stations) . The likelihood your radio will be tuned to a station that plays the song. . The likelihood you'll be thinking of the song at a randomly selected time of day. (Remember that if the song gets a lot of airplay it's more likely that you'll be thinking of it.) If the combined events were to occur once, would the probability present compelling evidence that the event wasn't merely a chance occurrence? What if it happened twice in one day? Three times in one day?Explanation / Answer
Here we are supposed to answer the probability of turning on the radio (event1) and Listen the song which you want to hear(event1).
Here you can see in the above sentence and between two bold letters which is of utmost importance as we need to find theprobability of intersection of event1 &2 .
So now lets bring it down in your context
Factor 1: likelyhood you would hear a song during randomly slected time . So in my context I hear radio in my car when I travel for office and so it takes total 2 hrs to reach my office and during that time my song comes approx 1 time on radio which takes approx 5 mins to conclude so., the probability of factor 1 = 5/(2*60) =1/24
Factor 2: likelyhood that the radio will be tuned to a station that plays the song.
We have 6 stations and so the probability of the radio will be tuned to a station that plays the song = 1/6
Factor 3: The likelyhood of thinking of the song at randomly selected time of a day
so., the probability here is like I generally think of 30mins in a day for the song and so the probability = 30/(24*60) =1/48
where 24*60 is the number of minutes of the day (24 hrs * 60mins/hr = 24*60 mins)
So the combined probability = P(Factor 1) * P(Factor 2) * P(Factor 3) = 1/24 * 1/6 * 1/48 = 0.0001446759
Which is very less 0.0001446759 i.e. 0.015% approx
So since the probability is 0.015% which is very less and so we can say that since it is very low so it could merely be a chance occurrence
The probability of happening the event twice in 1 day = 0.0001446759 ^2 = 2.093112 X 10^-8 which is very less.
The probability of happening the event thrice in 1 day = 0.0001446759 ^3 = 3.028228 X 10^-12 which is very less.
Hope the above answer has helped you in understanding the proble. Please upvote the ans if it has really helped you. Good Luck!!
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