>the probability of change in each system might not be high, but overall probability of general change is much higher - because it's multiplication of individual probabilities.
I get what the author is trying to say, but they had this one backward. Probabilities get smaller by multiplication. What he probably had in mind is :
- The probabilities of change events C1,...,Cn is P1,...,Pn
- The probability of no change at all is therefore (1-P1)(1-P2)...(1-Pn), which does indeed become smaller as more (independent) events C1,..., Cn are accounted for. And therfore the probability of change increases, but not because its a multiplication of probabilities, the exact opposite in fact, its because 1 - <multiplication of multiple probabilities>.
- Another way of phrasing the above is that, although each Pi might be small, their sum represents a sizable chunk of 1,therefore a significant probability. This only holds if events intersects minimally or not at all. This is a different assumption than that of independence.
I get what the author is trying to say, but they had this one backward. Probabilities get smaller by multiplication. What he probably had in mind is :
- The probabilities of change events C1,...,Cn is P1,...,Pn
- The probability of no change at all is therefore (1-P1)(1-P2)...(1-Pn), which does indeed become smaller as more (independent) events C1,..., Cn are accounted for. And therfore the probability of change increases, but not because its a multiplication of probabilities, the exact opposite in fact, its because 1 - <multiplication of multiple probabilities>.
- Another way of phrasing the above is that, although each Pi might be small, their sum represents a sizable chunk of 1,therefore a significant probability. This only holds if events intersects minimally or not at all. This is a different assumption than that of independence.