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awarded  Student
Sep
28
revised Probability of predicting, then throwing, a particular multiset for 5 dice.
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28
awarded  Scholar
Sep
28
accepted Probability of predicting, then throwing, a particular multiset for 5 dice.
Sep
28
comment Probability of predicting, then throwing, a particular multiset for 5 dice.
Oh! That is really helpful to point out. It's becoming pretty clear that the fact that it's predicted doesn't end up changing the probability. In the case with two dice, it is easy to calculate that there are 6 ways to come up with pairs from 36 combinations. However for the 5 dice scenario, the 5 original combinations would have to become 38880 in order to maintain probability. Counting this isn't quite clear to me but I can try and figure it out later tonight and perhaps post a follow up question if I can't puzzle it out. Thanks for all of your help!
Sep
28
comment Probability of predicting, then throwing, a particular multiset for 5 dice.
@Steven Stadnicki - but the whole point is that you don't guess '1' every time. If the guess on every roll is random, what's the difference between rolling two dice and seeing if they're the same? One die could be considered the guessing die.
Sep
28
awarded  Editor
Sep
28
comment Probability of predicting, then throwing, a particular multiset for 5 dice.
Actually, after thinking about it, it seems correct to square the probability. He chose his prediction seemingly at random and then rolled it immediately. Doing this with one die, where you make a new random prediction before every roll, you'd have a $1 \over 36$ probability of being successful on any given attempt, right?
Sep
28
revised Probability of predicting, then throwing, a particular multiset for 5 dice.
added 683 characters in body
Sep
28
comment Probability of predicting, then throwing, a particular multiset for 5 dice.
Oh, wow. The prediction aspect doesn't contribute to the probability anything more than that it specifies one roll. For some reason I was convinced it made the probability smaller to have predicted the roll beforehand. Thank you for explaining! Man, I'm bad at math lol
Sep
28
awarded  Supporter
Sep
28
comment Probability of predicting, then throwing, a particular multiset for 5 dice.
Thanks for your input on the first paragraph! However in the second paragraph I don't quite follow what the difference is between making a prediction and then getting that outcome vs. a prediction coming true. Isn't that the same thing?
Sep
28
asked Probability of predicting, then throwing, a particular multiset for 5 dice.