Followup: tinfoil hats & probability

The last post said 2/44 and 5/114 were "about what chance would predict" in telling whether a cell tower was on based on subjective feelings. That evaluation is taken from the BBC article linked in that post.

If the tower is on about half the time, a random guess has about a 50/50 chance of being right. In that case, correctly guessing 6 times out of 6 has a probability of 1 in 2 to the 6th power, or 1 in 64.

On the other hand, suppose the tower is on more than half the time; say, three-quarters of the time. Therefore, if you always guessed "on," you'd be right about 3/4 of the time. The probability of guessing correctly six times out of six when you have a 3/4 chance of being right is about 1 in 5.6.

So the probability of guessing correctly is a function of how much of the time the tower is on. And that information (not directly provided in the article) is what tells you whether 2/44 (4.545%) and 5/114 (4.386%) is "about what chance would predict" or not. The similarities of the proportions (4.4 +/- 0.1%) is a pretty good indication they're drawing from the same population, though.