Question Number 106405 by john santu last updated on 05/Aug/20
$$\mathrm{A}\:\mathrm{bag}\:\mathrm{contains}\:\mathrm{6}\:\mathrm{white},\:\mathrm{4}\:\mathrm{red}\:\&\:\mathrm{10} \\ $$$$\mathrm{black}\:\mathrm{balls}.\:\mathrm{If}\:\mathrm{two}\:\mathrm{balls}\:\mathrm{are}\:\mathrm{drawn} \\ $$$$\mathrm{at}\:\mathrm{random},\:\mathrm{what}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{probability}\:\mathrm{of}\:\mathrm{both}\:\mathrm{being}\:\mathrm{black}\:? \\ $$
Answered by bemath last updated on 05/Aug/20
$$\mathrm{p}\left(\mathrm{A}\right)\:=\:\frac{\mathrm{C}\:_{\mathrm{2}} ^{\mathrm{10}} }{\mathrm{C}\:_{\mathrm{2}} ^{\mathrm{20}} }\:=\:\frac{\mathrm{45}}{\mathrm{190}}\:=\:\frac{\mathrm{9}}{\mathrm{38}}\: \\ $$