3 ms·
Just to work out the odds, it's not 2^-8 since she knew there were four of each type of tea. 1 in 70 = 8 choose 4, which one can mental math as 8!/(4!4!) = 8765
by mxwsn 7y ago
Just to work out the odds, it's not 2^-8 since she knew there were four of each type of tea. 1 in 70 = 8 choose 4, which one can mental math as 8!/(4!4!) = 8765/4! = (8/(42))7(6/3)5*1 = 70.
My asterisks got formatted :( still works though
- hooloovoo_zoo 7y agoAccording to the story she chose after each cup, not at the end (so it's harder for her to make use of the 4-4 information); therefore, the odds calculation is not so straightforward right?
- max_likelihood 7y agoI was thinking the same thing! I think those would be her odds if she were permitted to go back and change her mind about which cups of tea had milk first. If she said the first 4 cups were milk first with some confidence, but on the fifth cup was absolutely certain it was milk first, she would have to go back and change a previous evaluation (because she knows there can be only 4). But because they were presented one at a time, and Bristol made her determination up front. It's basically a series of independent Bernoulli trials (i.e. Binomial distribution). So, assuming she had a 50% chance of guessing correctly, the probability would be (8 choose 4) * (1/2)^8.