Question : A urn contain N white and M black balls. Balls are randomly selected, one at a time , until a black one is obtained . It we assume that each selected ball is replaced before the next one is drawn, what is the probability that
i) exactly n draws are needed
ii) atleast k draws are needed
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Should i be using geometric distribution
Hello, zorro!
Who wrote this problem?
What a confusing set of variables!
Let , the total number of balls.An urn contains white and black balls.
Balls are randomly selected, one at a time , until a black one is obtained.
Each selected ball is replaced before the next one is drawn.
Find the probability that:
a) exactly draws are needed.
b) at least draws are needed.
Should i be using geometric distribution? . . . . no
Since the balls are replaced, the probabilities remain constant.
. .
(a) A black ball is drawn on the draw.
. . .The first balls are White, the is Black.
. . .
(b) At least draws.
We have this list of possible outcomes:
. .
Our probability is the sum of these probabilities:
. . . . . . . . . . . . .[1]
Substitute into [1]:
. .