MathBlog: Kid A and B (Every Boy In His Right Place)

[combinator]

I think this problem is worth thinking about even if you don't think of yourself as a math person (and especially in that case trying the penny flipping game). I first heard about it in the "Ask Marilyn" column

Comments

[leko]

Interesting. I think the fact that the first answer gives a sort of aside example, it seems like the more likely answer. Also, I think the fact that it's an easy and reasonable conclusion, and it comes before the convoluted conclusion, makes it more likely to be chosen.

Anyway, I'm sort of interested in knowing the 'value' of knowledge on probability. In this example the value is 1/12 (1/3-1/4). If there were 3 equally possible outcomes, the value of knowing one of them 4/45 (1/5-1/9) .

So I was curious of the answer to "what is the value of knowing one outcome of a series of random, independent, outcomes in determining the probability of all outcomes being equal." Of course I'm also curious about the value of knowing one outcome wrt determining the probability of any combination of outcomes (rather than the specific permutation, as I have now), but I need to shower and go to work.

anyway, what I came up with wasn't very hard, but I haven't thought about any of this in a long time, so I was starting from scratch. does it look right?

n=number of equally possible outcomes
r=number of iterations

Value = (1/n)^r/(1-((n-1)/n))^r) - (1/n)^r