a probability problem

Mohammad Hashemian · science forum beginner Joined: 16 Apr 2006 Posts: 2

Hello,
Previous week I see a problem that can be solved by Law of Total
Probability Theorem, my teacher said that I should solve this problem
in some way else, like Poisson theorem.
here is the problem:

we have two boxes. there is six white balls and four black balls in
first box and five white balls and seven black balls in second box.
then we pick up four balls randomly from second box, and take them away
without seeing their colors. now we pick up remaining balls from second
box and insert them into first box. so we don't know how many black
balls or white balls is in first box. now we pick up a ball from first
box randomly. now I wantto know the probability that this ball is
white.

now I want to know how can I solve this problem or how can I
partitioning the sample space of this problem? I know one way for this,
that we calculate all conditions that 4 balls have. for example 0 white
ball and 4 black balls, 1 white ball and 3 black balls and .... but I
sould partition the sample space in some way else.
Excuse me for my poor english, Idon't know the probability terminology
in english.
regards,
Muhammad Hashemian

Mike Terry · science forum Guru Wannabe Joined: 02 May 2005 Posts: 137

"Mohammad Hashemian" <m.hashemian@gmail.com> wrote in message
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