Probability problems

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Probability problems
Message posted by Poulami on November 28, 2000 at 12:00 AM (ET)

1. An urn contains N1 white, N2 black and N3 red balls. Balls are successively drawn without replacement until a red ball is drawn. Find the probability that:

a) n1 white and n2 black balls are drawn.

b) not a single white ball is drawn

c) a total of k balls are drawn.

( I am having problem with part a especially. So please explain that at least in detail)

2. A man has n keys, one of which fits a lock. He tries the keys one at a time , at each trial choosing at random from the keys that were not tried earlier. Find the probability that the key tried at the rth trial is the correct key.

3. n indistinguishable balls are distributed without replacement among M (>n) urns numbered 1 to M . Determine the probability that each urn numbered 1 to n contains exactly one ball.

READERS RESPOND:
(In chronological order. Most recent at the bottom.)

Re: Probability problems
Message posted by nancy diehl on November 30, 2000 at 12:00 AM (ET)

I haven't done probablity in awhile, but possibly can give you some direction.
Problem 1 is a hypergeometric probablity problem. Look the formula up for the setup.
It uses the Combination formula and your denominator is the combination of N choose n
where N is the total number of balls in the urn (6?) and "n" is the sample size being
drawn (in part a you are drawing 3 balls). The numerator is setup with combination
formulas for the subsets of the items and how many of each are to be drawn. So for part
a you have the combination of "1 choose 1" for the white and "2 choose 2" for the black and
"3 choose 0" of the red. Again, see a reference book on using the hypergeometric formula.

For problem 3, I don't know the formula off the top of my head, but I can tell
you that's a direct application of what is call "The pidgeon hole principle". Again,
find a reference on this principle and it should be straight-forward from there.

Re: Probability problems
Message posted by Poulami on December 1, 2000 at 12:00 AM (ET)

Hi.Thanks. What is the pidgeon hole principle? I found what is Bose-Einstein Statistics for distinguishable events but could not proceed much.

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