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On 13/01/2011 02:27 PM, Invisible wrote:
> Suppose the probability of a catch is unconditionally P. How does the
> length of a typical series of consecutive catches vary as a function of P?
Apparently catching or dropping the diabolo can be regarded as a
Bernoulli trail, and thus performing an open orbit is a kind of
Bernoulli process. In particular, the number of failures before a
success is achieved (or, conversely, the number of successes before the
first failure) follows a geometric distribution.
Specifically, if the probability of catching the diabolo is P, then the
probability of *not* catching it must be 1-P. Apparently the probability
of K successes followed by one failure is
Prob K = P^K * (1-P)
Thus, each series of catches of length K+1 is a factor of P less
probable than a series of length K.
All of this of course assumes that the trails are *independent*, which
they manifestly are not...
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