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A-box-contains-12-balls-numbered-from-1-to-12-4-balls-are-selected-successively-without-replacement-Given-X-the-variable-the-number-of-even-numbered-balls-selected-Determine-the-probability-typ




Question Number 105934 by Ar Brandon last updated on 01/Aug/20
A box contains 12 balls numbered from 1 to 12. 4 balls  are selected successively without replacement. Given  “X” the variable “the number of even numbered balls  selected”. Determine the probability type/law of X.
$$\mathrm{A}\:\mathrm{box}\:\mathrm{contains}\:\mathrm{12}\:\mathrm{balls}\:\mathrm{numbered}\:\mathrm{from}\:\mathrm{1}\:\mathrm{to}\:\mathrm{12}.\:\mathrm{4}\:\mathrm{balls} \\ $$$$\mathrm{are}\:\mathrm{selected}\:\mathrm{successively}\:\mathrm{without}\:\mathrm{replacement}.\:\mathrm{Given} \\ $$$$“\mathrm{X}''\:\mathrm{the}\:\mathrm{variable}\:“\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{even}\:\mathrm{numbered}\:\mathrm{balls} \\ $$$$\mathrm{selected}''.\:\mathrm{Determine}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{type}/\mathrm{law}\:\mathrm{of}\:\mathrm{X}. \\ $$
Answered by bobhans last updated on 01/Aug/20
even number = { 2,4,6,8,10,12}  p = (6/(12)) = (1/2). P(X=x) = Σ_(x=0) ^4 C _x^4  ((1/2))^x ((1/2))^(4−x)
$$\mathrm{even}\:\mathrm{number}\:=\:\left\{\:\mathrm{2},\mathrm{4},\mathrm{6},\mathrm{8},\mathrm{10},\mathrm{12}\right\} \\ $$$$\mathrm{p}\:=\:\frac{\mathrm{6}}{\mathrm{12}}\:=\:\frac{\mathrm{1}}{\mathrm{2}}.\:\mathrm{P}\left(\mathrm{X}=\mathrm{x}\right)\:=\:\underset{\mathrm{x}=\mathrm{0}} {\overset{\mathrm{4}} {\sum}}\mathrm{C}\:_{\mathrm{x}} ^{\mathrm{4}} \:\left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{x}} \left(\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{4}−\mathrm{x}} \\ $$
Commented by Ar Brandon last updated on 01/Aug/20
OK. But I felt the probability of selection on each trial  isn′t same.
$$\mathrm{OK}.\:\mathrm{But}\:\mathrm{I}\:\mathrm{felt}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{of}\:\mathrm{selection}\:\mathrm{on}\:\mathrm{each}\:\mathrm{trial} \\ $$$$\mathrm{isn}'\mathrm{t}\:\mathrm{same}. \\ $$

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