Recent content by Ursole

No doubt it is provable, but I don't know of one. Thanks for the tip. .

Can it be further improved? No, seems like we can't escape from having 4 false negatives and 1 false positive. The formatting below didn't come out well here. The totals are the sum of Prob. Let probability partner says n = PPSn Let probability of guessing right = PGR Let PGR * PPSn...

However, it is possible to improve on 5/6!

But your strategy should also include you and your partner agreeing always to call the higher [or lower] number. Then I make make the probability of being right equal to (5/6)(4/5) + (1/6)(6/6) = 5/6 Do you agree? .

Sorry, AKG. I forgot the wording of the puzzle. :redface:

If you always call 'not summing to 7, then you will be right every time a double is thrown. .

I don't agree with your 9/11 perhaps you are forgetting about doubles.

Let n = number of times the coin is flipped. I open a box and see 3^a dollars, where a > 1. I know n = a or a-1, and Prob(n = a) is half of Prob(n = a-1); Prob(n = a) = 1/3 Prob(n = a-1) = 2/3 By the way, an 'optimum' strategy of always switching violates symmetry. .

Captain, this is not logical. [It is a personal opinion.] .

If the partner has to say "I see at least one of n" where n is the value of one of the two dice that were cast and then you have to say "the sum equals 7" or "the sum does not equal 7", what strategy could you and your partner decide upon, before starting the game, that would optimize your...

While it's true that the probability of picking the box with the larger amount is 1/2, the conditional probability that the other box contains more money given that the first box contained a dollars is 1 if a = 3 and 1/3 otherwise. So if you find a (a > 3) in the box and stick, you get a...

You are given that: Pure philosophers always tell the truth concerning their beliefs. Applied philosophers always lie concerning their beliefs. Sane philosophers beliefs are always correct. Insane pilosophers beliefs are always incorrect. Four philosophers {A,B,C,D}) have the...

The probability of rolling a 7 with a pair of ordinary dice is 1/6 because, of the 36 possible (and equally likely) combinations, six of them sum to 7. Now, suppose the dice are rolled out of one's sight and some honest person who can see the result tells us that at least one of the dice came up...

Assume I flip a fair coin n times until it comes up Heads. Now I take two large boxes, in one of which I place $3^n (3 to the power of n dollars) and in the other I place $3^(n+1) (3 to the power of n+1 dollars). I then give you the two closed seemingly identical boxes and allow you to open one...

I thought this was a forum.