<PRE><B>Question 345439</B>
let D=event of detecting large amount of liquid or positive test
let L=event of bag containing large amounts of liquid
let S=event of bag containing small amounts of liquid
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given
P(D/L)=0.92
P(D/S)=0.1
P(L)=3/100=0.03
Need to find P(D)
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P(S)=1-P(L)=1-0.03-0.97
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P(D)=P(D and L)+P(D and S)
    =P(D/L)*P(L)+P(D/S)*P(S)
    =0.92*0.03+0.1*0.97
    =0.0276+0.097=0.1246</PRE>