This is based on two previous polls:
/Toby96/what-is-your-intuition-about-this-p-c937e06a9ba2
/KongoLandwalker/what-is-your-intuition-about-this-p
The difference is that I am using a larger probability than either of them.
We have two different independent potential events A and B. Someone tells you, "The probability of A is .75. B is two times more likely than A."
There are at least three ways to intepret this sentence:
"Multiply the probability": The probability of B is 1.5 (2 times the probability of A). Under this interpretation, it's impossible for the sentence to be true.
"Multiply the chances": We imagine that there are 100 tickets in a hat, and 75 of them represent event A, with 25 representing not A. "B is two times more likely" means that the hat for B has twice as many B tickets as there were A tickets, but the same number of "not B" tickets. I.e., the probability is (2*75)/(2*75+25) ≈ .857.
"Halve the probability of not occuring": For events with probability > 0.5, doubling the liklihood means that you divide the chance of it not happening by 2. So the probability is 1 - (1 - .75)/2 = .875.