The probability a given solution is valid to a given problem is p. The probability that a given solution is invalid is 1−p. The probability that all are invalid is (1−p)n. The probability that not all are invalid (there is some solution) is 1−(1−p)n.
The probability that all problems are solved is (1−(1−p)n)n. The probability of doom (that not all problems are solved) is 1−(1−(1−p)n)n.
For p=0.5, n=1000, Google thinks this number is 0.
Yep, the crux is: do we need a unique solution which solves all our problems, or can we accept that different problems are solved by different solutions? I somewhat lean to the former.
The probability a given solution is valid to a given problem is p. The probability that a given solution is invalid is 1−p. The probability that all are invalid is (1−p)n. The probability that not all are invalid (there is some solution) is 1−(1−p)n.
The probability that all problems are solved is (1−(1−p)n)n. The probability of doom (that not all problems are solved) is 1−(1−(1−p)n)n.
For p=0.5, n=1000, Google thinks this number is 0.
Yep, the crux is: do we need a unique solution which solves all our problems, or can we accept that different problems are solved by different solutions? I somewhat lean to the former.
Oh I see how the formula follows from that assumption.