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Question Number 179906 by Acem last updated on 04/Nov/22

2 boxes, 1st contains 4 white & 6 black balls 2nd box contains 8 white & 8 black balls We randomly draw a ball, got a black one What′s probability that it was drawn from Box_2 ?

$$\mathrm{2}\:{boxes},\:\mathrm{1}{st}\:{contains}\:\mathrm{4}\:{white}\:\&\:\mathrm{6}\:{black}\:{balls} \\ $$$$\:\mathrm{2}{nd}\:{box}\:{contains}\:\mathrm{8}\:{white}\:\&\:\mathrm{8}\:{black}\:{balls} \\ $$$$\:{We}\:{randomly}\:{draw}\:{a}\:{ball},\:{got}\:{a}\:{black}\:{one} \\ $$$$\:{What}'{s}\:{probability}\:{that}\:{it}\:{was}\:{drawn}\:{from}\:{Box}_{\mathrm{2}} ? \\ $$

Answered by som(math1967) last updated on 04/Nov/22

P(Box_1 )=P(Box_2 )=(1/2) Probability drawn from Box_2 =(((1/2)×(8/(16)))/((1/2)×(6/(10))+(1/2)×(8/(16))))=((8/(16))/((48+40)/(80))) =(8/(16))×((80)/(88))=(5/(11))

$${P}\left({Box}_{\mathrm{1}} \right)={P}\left({Box}_{\mathrm{2}} \right)=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$${Probability}\:{drawn}\:{from}\:{Box}_{\mathrm{2}} \\ $$$$\:=\frac{\frac{\mathrm{1}}{\mathrm{2}}×\frac{\mathrm{8}}{\mathrm{16}}}{\frac{\mathrm{1}}{\mathrm{2}}×\frac{\mathrm{6}}{\mathrm{10}}+\frac{\mathrm{1}}{\mathrm{2}}×\frac{\mathrm{8}}{\mathrm{16}}}=\frac{\frac{\mathrm{8}}{\mathrm{16}}}{\frac{\mathrm{48}+\mathrm{40}}{\mathrm{80}}} \\ $$$$=\frac{\mathrm{8}}{\mathrm{16}}×\frac{\mathrm{80}}{\mathrm{88}}=\frac{\mathrm{5}}{\mathrm{11}}\: \\ $$

Commented by Acem last updated on 04/Nov/22