4 ms·
Remember the principle of conservation of expected probability. P[X] = P[X|Y] * P[Y] + P[X|!Y] * P[!Y] . If P[X|Y] > P[X] and P[Y] is strictly between 0 and 1,
by drdeca 2y ago
Remember the principle of conservation of expected probability. P[X] = P[X|Y] * P[Y] + P[X|!Y] * P[!Y] .
If P[X|Y] > P[X] and P[Y] is strictly between 0 and 1, then P[X|!Y] < P[X] .
So, if X is “dark matter is some kind of matter that can be detected directly” and Y is “Dark matter is/would-be detected directly by this experiment (when/if the experiment is/would-be done)” then, if we do the experiment and it does not directly detect dark matter, then, if we previously assigned some positive probability that it would, our probability that we can detect it in some way, should go down (though not necessarily by a non-negligible amount).
- deleted 2y ago[deleted]