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Question Number 105934 by Ar Brandon last updated on 01/Aug/20

$$\mathrm{A}\mathrm{box}\mathrm{contains}12\mathrm{balls}\mathrm{numbered}\mathrm{from}1\mathrm{to}12.4\mathrm{balls}$$$$\mathrm{are}\mathrm{selected}\mathrm{successively}\mathrm{without}\mathrm{replacement}.\mathrm{Given}$$$$‘‘{\mathrm{X}}^{″}\mathrm{the}\mathrm{variable}‘‘\mathrm{the}\mathrm{number}\mathrm{of}\mathrm{even}\mathrm{numbered}\mathrm{balls}$$$${\mathrm{selected}}^{″}.\mathrm{Determine}\mathrm{the}\mathrm{probability}\mathrm{type}/\mathrm{law}\mathrm{of}\mathrm{X}.$$

Answered by bobhans last updated on 01/Aug/20

$$\mathrm{even}\mathrm{number}=\{2,4,6,8,10,12\}$$$$\mathrm{p}=\frac{6}{12}=\frac{1}{2}.\mathrm{P}(\mathrm{X}=\mathrm{x})=\underset{\mathrm{x}=0}{\sum ^4}\mathrm{C}{}_{\mathrm{x}}^4{\left(\frac{1}{2}\right)}^{\mathrm{x}}{\left(\frac{1}{2}\right)}^{4-\mathrm{x}}$$

Commented by Ar Brandon last updated on 01/Aug/20

$$\mathrm{OK}.\mathrm{But}\mathrm{I}\mathrm{felt}\mathrm{the}\mathrm{probability}\mathrm{of}\mathrm{selection}\mathrm{on}\mathrm{each}\mathrm{trial}$$$${\mathrm{isn}}^{\prime }\mathrm{t}\mathrm{same}.$$

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