# Probability over probability

Discussion in 'Scientific Statistics Math' started by Amoz Puu, Jul 21, 2003.

1. ### Amoz PuuGuest

Say there are 1 million pebbles. Some black and some are white.

You take 100. 50 are blacks, 50 are white. What is the probability
that another one is black?

You take 100, all 100 are blacks, what is the probability that another
one is black?

You take 1, that one is black. What is the probability that another
one is also black?

We are taught to estimate the probability of something based on its
frequency.

For example, if we do 100 experiment and 100 are black, than the
probability that everything is black is 100/100=1. However, this
estimate also has uncertainty. It is possible that we happen to take
100 black pebbles. It is possible that the rest are white and only 100
are black, and the 100 that we pick happen to be the black ones. This
issue raise in live a lot where people are basing their map on the
world on their experiences and there is only so much data.

So, how do we deal with this probability within probability? Do we say
that if we do 100 experiment and 100 are black, than the probability
of the next one is black would be 99%? I mean it should be less than
100% but it should be close to 1 because so far all are black right?

What would be the formula? Can I extend it to few cases? What about if
someone take 1 pebbles and found a black one?

Amoz Puu, Jul 21, 2003

2. ### Duncan SmithGuest

Have a Google for Bayes Rule.

Duncan

Duncan Smith, Jul 21, 2003

3. ### Ron LarhamGuest

You need to lookup Bayes theorem/Baysian ststistics

RonL

Ron Larham, Jul 21, 2003
4. ### W. D. Allen Sr.Guest

For probability theory to apply to real world problems two
conditions must exist.

First, all the elements in the population in question must
be homogeneous, for example, only marbles, not part marbles
and part beads, when evaluating the distribution of the
colors of marbles.

The second requirement is that the population must be truly
randomized, i.e., each element in the population must have
equal likelihood of selection [and how often does this
condition truly occur in the real world?].

Only then will all those probability equations truly apply!

Good luck!

WDA

end

W. D. Allen Sr., Jul 21, 2003