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Expected number of balls to select
Hi I have this question. There is a huge urn with balls in 5 different colors. I pick one. What is the expected number of balls I need to pick to get a ball with the same color as the first ball in the following two cases:(i) each color is 20% of the balls.(ii) balls of color i occur with p_i.
Expected number of balls to select
The general form (ii) is:In this case n = 5 and thus:in the specific uniform case (i) where
Expected number of balls to select
Your answer looks wrong.How do you get that?
Expected number of balls to select
Well I think it is (1/My answer) = # of balls to select. But explain how it is wrong/ give a counter example.
Expected number of balls to select
I think this problem can be set up recursively.For i), if we define the event of picking up a ball of the same color as the first as A, then... E[A] = (1/5)(1) + (4/5)(E[A]+1) => (1/5)E[A] = 1 => E[A] = 5For ii), we generalize the results from i)... E[A] = (p_i)(1) + (1-p_i)(E[A] + 1) => (p_i)E[A] = 1 => E[A] = 1/p_iOf course, the above method is working under the assumption that the distribution of picking up a specific colored ball doesn't change (aka a large urn with a huge number of balls).
Last edited by cvkmndfv on October 26th, 2010, 10:00 pm, edited 1 time in total.
Expected number of balls to select
Heh good one. ps: great trick cvkmndfv, will utilize in the future