What is your intuition about this probability comparison (large probability)?
Never closes
~ .857

This is based on two previous polls:



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:

  1. "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.

  2. "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.

  3. "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.

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I voted for 1.5, but I would prefer to state my intuition as being that the "someone" has told me something that is not true.

@Fion Yes, of course if they told you the probability is 1.5, then it isn't true.