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Imagine we have 2 slots that can be sequentially occupied (2nd slot only after the 1st one) by (let's say) squirrels. Each slot has its own probability of being occupied: 1st slot can be occupied with p1= 0.1 and the second with p2= 0.6. I am wondering what is the probability of these 2 slots being occupied. If we have only 2 squirrels than this probability is p1*p2. I have troubles to figure out what this probability will be if there are N squirrels.

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This is textbook conditional probability. The probability of N squirrels is given by product(p-1,...,p-n). Now if you're asking about how to obtain the probability for each successive slot in the sequence, you'll need to calculate it from the observed distribution.

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  • $\begingroup$ Thanks! Product of probabilities will not work for the computing probability for the last slot, because they are not independent. What's the way to derive this disruption? $\endgroup$
    – Sp_J
    Commented Jul 13, 2018 at 15:52

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