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Math Help - Probability for two people to listen to the same song

  1. #1
    M_P
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    Probability for two people to listen to the same song

    Hello everyone!
    I've been thinking about this problem for the last few days, but I cannot find a valid answer, so I hope that someone else can help me out!
    Let's start saying that it is not a school-related problem at all, I've just thought about it by myself.

    Let's consider the setting where we have N people, each one with his/her own iPod (or another mp3 player).
    If we put the iPod on shuffle mode, which is the probability that, when me and another person press the 'next song' button, we listen to the same song?
    Let's consider the songs as statistically independent.

    I think that, if we consider the set of all possible songs as infinite, the probability should be zero. Am I right?

    Now, if we consider the problem when the set of possible songs is finite (let's call it S songs), is it better for me to have just one song on the iPod, or to have a lot of songs, in order to maximize the probability?

    I'm looking forward for any suggestion!
    Thank you!

    M_P
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  2. #2
    Flow Master
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    Quote Originally Posted by M_P View Post
    Hello everyone!
    I've been thinking about this problem for the last few days, but I cannot find a valid answer, so I hope that someone else can help me out!
    Let's start saying that it is not a school-related problem at all, I've just thought about it by myself.

    Let's consider the setting where we have N people, each one with his/her own iPod (or another mp3 player).
    If we put the iPod on shuffle mode, which is the probability that, when me and another person press the 'next song' button, we listen to the same song?
    Let's consider the songs as statistically independent.

    I think that, if we consider the set of all possible songs as infinite, the probability should be zero. Am I right?

    Now, if we consider the problem when the set of possible songs is finite (let's call it S songs), is it better for me to have just one song on the iPod, or to have a lot of songs, in order to maximize the probability?

    I'm looking forward for any suggestion!
    Thank you!

    M_P
    Read section 6.3 here: Birthday problem - Wikipedia, the free encyclopedia
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  3. #3
    M_P
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    Quote Originally Posted by mr fantastic View Post
    Thank you for your reply!
    I've understood the birthday problem, but I can apply it to my problem only if all the people have the same number of songs in the mp3 player.
    Moreover, we are sure that everyone's birthday is in the considered range of 365 days, while for the songs we don't know if we share any song...
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