SOLUTION: A box contains two red chips and three white chips. Let X denote the number of draws until a red chip is selected. (1) Find the discrete pdf for X if the chips are drawn at rand

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Question 342367: A box contains two red chips and three white chips. Let X denote the number of draws until a red chip is selected.
(1) Find the discrete pdf for X if the chips are drawn at random, with replacement.

Answer by jrfrunner(365) About Me  (Show Source):
You can put this solution on YOUR website!
since the drawing is with replacement
the probability of selecting a red is constant.
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Let prob(red)=p=2/5 , let prob(white)=1-p=3/5
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If X represent number of draws until the first success, ie selecting the first red,
then the pdf of X implies that there will be X-1 failures and the last one will be a success
P%28X=x%29=%281-p%29%5E%28x-1%29p=%283%2F5%29%5E%28x-1%29%282%2F5%29 for x>0
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this is the geometric probability distribution, since is sequence increases geometrically