Re: crocksucker solution
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hmm, let me take a shot...
the ratio between the probability of (x+1) tails and x tails should remain constant for all x. therefore, since the probability of getting 0 tails is 1/4, the ratio must be 3/4 in order to make the sum of the infinite series equal to 1.
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Good observation I think, and knowing that carries you to the answer of the original question.
The ratio of the terms in the probability distribution of getting to each flip is 3/4, but the expected number of Tails has each term in that sum weighted by the number of Tails . Ie E(T)=(0*1/4 + 1 * (1/4 * 3/4) + (2 * 1/4 * (3/4)^2)....
Using the methodology in the dice thread the answer to the expected number of Ts is 3. Is that reasonable?
P(0)=1/4
P(1)=3/16
P(2)=9/64
P(3)=27/256
P(4)=81/1024
P(5)=and so on
Weighting the probabilities by that number of Ts till T=10 gets to 2.4 o 2.5 (I did the math fast and got 2 different answers) so taking it to infinity looks close to 3 to me.
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