Buying ice cream question

**usagi_killer** · April 13th 2009, 08:30 PM

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 $37\%$ 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 !

**JohnQ** · April 14th 2009, 06:34 AM

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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