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Math Help - Buying ice cream question

  1. #1
    Senior Member
    Apr 2009

    Buying ice cream question

    Jack is walking around in Luna Park, and notices an alleyway called 'Infinite Ice Cream'. Jack notes that the 'Infinite Ice-Cream' appears to possess an infinitely large number of people selling ice-cream. Upon walking outside any particular shop, Jack feels a huge compulsion to purchase an ice-cream. For every shop that Jack visits, he is less likely to purchase an ice-cream then at the previous shop. After purchasing an ice-cream, Jack leaves Luna Park. What is the probability of Jack purchasing an ice-cream at the second shop he visits?

    Thanks guys !
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  2. #2
    Apr 2009
    Not an answer, since I haven't worked it out. But here is how I see the problem setup.

    w_n = a^{n-1} w_1

    The probability that he buys at the n-th shop is

    p_n = w_n \prod_{i=1}^{n-1} (1-w_i)

    You also know that \sum p_i = 1.

    Hopefully, all this could be used to solve the problem.
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