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Question Number 90196 by Ar Brandon last updated on 21/Apr/20

A bag contains 5 balls, 2 green and 3red  They are selected without replacement till  the remaining balls in the bag are of same colours.  Let the random variable X be the number  of selections possible  1) Determine the set of values of X  2)Determine the it′s expectation, its variance  and its standard deviation.

$$\mathrm{A}\:\mathrm{bag}\:\mathrm{contains}\:\mathrm{5}\:\mathrm{balls},\:\mathrm{2}\:\mathrm{green}\:\mathrm{and}\:\mathrm{3red} \\ $$$$\mathrm{They}\:\mathrm{are}\:\mathrm{selected}\:\mathrm{without}\:\mathrm{replacement}\:\mathrm{till} \\ $$$$\mathrm{the}\:\mathrm{remaining}\:\mathrm{balls}\:\mathrm{in}\:\mathrm{the}\:\mathrm{bag}\:\mathrm{are}\:\mathrm{of}\:\mathrm{same}\:\mathrm{colours}. \\ $$$$\mathrm{Let}\:\mathrm{the}\:\mathrm{random}\:\mathrm{variable}\:\mathrm{X}\:\mathrm{be}\:\mathrm{the}\:\mathrm{number} \\ $$$$\mathrm{of}\:\mathrm{selections}\:\mathrm{possible} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{Determine}\:\mathrm{the}\:\mathrm{set}\:\mathrm{of}\:\mathrm{values}\:\mathrm{of}\:\mathrm{X} \\ $$$$\left.\mathrm{2}\right)\mathrm{Determine}\:\mathrm{the}\:\mathrm{it}'\mathrm{s}\:\mathrm{expectation},\:\mathrm{its}\:\mathrm{variance} \\ $$$$\mathrm{and}\:\mathrm{its}\:\mathrm{standard}\:\mathrm{deviation}. \\ $$

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