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For an event to occur, in an interval of...
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For an event to occur, in an interval of 28 days, you have a chance of 0 for the first 23 days and then chances [math] p_1, p_2, p_3, p_4, p_5 [/math] (each in [0,1], no correlation between the p_i's) in the remaining 5 days.

You probe this setup at a random day, the particular day you choose is given by a probability P (with [math] \sum_{n=1}^{28} P(n) = 1 [/math]).

What are the chances for the event to occur?

For starters, I think for P(n)==1/28 constant, you get
[math] \dfrac {1} {28} \sum_{n=i}^{5} p_i [/math],
but that's just my intuition.
>>
>>7809341
if the sum of probabilities over 28 days is 1 and the probabilities of the first 23 are 0 then the sum of probabilities over the last 5 days are 1, so the probability of it happening in those days is 1...

Assuming they're equal, each day is 1/5 chance
>>
>>7809341
>What are the chances for the event to occur?
if do not ask about what time interval, since all your problem deals with time intervals, you have no answer to your problem.
>>
>>7809341
>a chance
>the chances
Lrn2probabilly
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