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the probability of 5 blocks within next 40 mins is 15%.
Do I understand it correctly then if I say that the probability of 5
or more blocks within the next 40 minutes (and therefore within the 40 minutes immediately following the broadcast of a block) is 26%?
The probability of 5
or more blocks within the next 40 minutes is 1 - N[CDF[PoissonDistribution[4], 4]] = 37%, I made a correction in my first reply, see striketrhough.
Since events are independent, it does not matter if you are just after a block or not.
Probability of 5 or more blocks includes probabilty of 5, probability of 6 ....
The way you deal with this is using cummulative probability function as I enumerated in the previous post. Using that table you can compute the probability of any block number range withing 3 hours.
Examples:
The probability of less or equal 15 blocks is 28.6 %
The probability of more than 20 blocks in 3 hours is 1-0.73072 = 26.9%
The probability of 16-20 blocks is 0.73072 - 0.286653 = 44.4%