<t>The problem to find E{N} for N(52,13).let's start with a simpler case N(3,1) to enumerate all combinations (which is C(3,1)), interested face is "1" and others ".", we count the remaining cards in the deck.1.. -> 2.1. -> 1..1 -> 0Let S is the sum of all remaining cards, 3 in this caseThe number w...
yep, the simplified formula is:p = P(boy born | boy selected) = (b + 1) / (2b + 1), where b is the number of boys initially.some special cases:b=0 -> p=1b->Inf -> p=0.5
your last two entries are not "obeying" the rule. 359369 The answer is 12.There are C(9,2) = 36 unique pairs of colors. Each flag represents C(3,2) = 3 such pairs, therefore there can be maximum 36/3 = 12 such flags.
More hints:For a 3 sided die (a rounded-off triangular prism will do) use these values 1,6,8b: 2,4,9c: 3,5,7here on average b beats a, c beats b, and a beats c.
<t>This works only for special dice. I guess it was on Scientific American some years ago. You can design the die such thata wins against b, b wins against c, and c wins against a. Note that the expected values will be the same but it's not the same as winning against.Exercise to you is to set up th...