a-box-contains-4-blue-3-green-and-2-red-identicall-balls-if-two-balls-are-selected-at-random-without-replacement-what-is-the-probability-that-two-balls-be-of-the-same-colours-

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Question Number 106292 by bemath last updated on 04/Aug/20

$$\mathrm{a}\mathrm{box}\mathrm{contains}4\mathrm{blue},3\mathrm{green}\mathrm{and}2\mathrm{red}\mathrm{identicall}\mathrm{balls}.$$$$\mathrm{if}\mathrm{two}\mathrm{balls}\mathrm{are}\mathrm{selected}\mathrm{at}\mathrm{random}\mathrm{without}$$$$\mathrm{replacement},\mathrm{what}\mathrm{is}\mathrm{the}\mathrm{probability}$$$$\mathrm{that}\mathrm{two}\mathrm{balls}\mathrm{be}\mathrm{of}\mathrm{the}\mathrm{same}\mathrm{colours}?$$

Answered by bobhans last updated on 04/Aug/20

$$\mathrm{p}\left(\mathrm{A}\right)=\frac{\mathrm{C}{}_2^4+\mathrm{C}{}_2^3+{\mathrm{C}}_2^2}{{\mathrm{C}}_2^9}=\frac{12+3+1}{36}=\frac{16}{36}=\frac{4}{9}$$

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