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Learning is tough


Learning is tough because, 
while a little knowledge that you're missing
can often bridge large gaps,
it is not accessible to you -
for if it was,
you would reach out

and grasp it.
And no one else can provide it,
because no one but you
knows exactly what you
know and don't know.

This is why we have few friends in
our neighborhoods,
just acquaintances
and strangers.



Solitude is precious


We are trained within our culture from the onset
of our lives to see things a certain way.
This is our cultural conditioning, and we often
adopt it without realizing it as such.
Almost always, we use good logic and the truths found within this
network to make judgments, decisions, and establish values.
Sometimes, we allow ourselves to believe in truths found
outside this network, which may (or may not) lie in
contradiction to ones inside it.
If we do so,
we think of the experience
as one of irrationality or spirituality.

For some,
it is a spiritual experience
that stems from and is guided by an outside source.


However, true happiness can be found by working on probability problems.

I found this about 8 years ago in a GNU book
called Chance Probability. It's not an elementary
problem, unless you make assumptions.
This problem originally appeared in:

K. L. Chung, Elementary Probability
Theory With Stochastic Processes, 3rd ed
(New York:Springer-Verlag, 1979), p. 152


Pickwick’s Umbrella

In London, half of the days have some rain. The weather forecaster is correct  2/3 of the  time, i.e., the probability that it rains, given that she has predicted rain,  and the probability that it does not rain, given that she has predicted that it won’t  rain, are both equal to 2/3. When rain is forecast, Mr. Pickwick takes his umbrella.  When rain is not forecast, he takes it with probability 1/3.

Can you find
(a) the probability that Pickwick has no umbrella, given that it rains.
(b) the probability it doesn’t rain, given that he brings his umbrella.


Note: You may not assume that the probability that she predicts rain is 1/2 or that the probability that she predicted rain given that it rains is 2/3; however, you need that, so prove it first.  

Hint: Show that for any two events R & F such that   a = P(R|F) = P(~R|~F)
 P(F)  =   1 - (a +P(R))  ,   
                  1 - 2a
a ≠ ½ and under the further constraints that place the RHS between 0 and 1 inclusive.
When P(R) = ½  a drops out of the RHS and P(F) = ½ .