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Three companies supply same type of products. Company A supplies 30 % more products than company B. Company C supplies the same as A. Fraction of defective products produced by company A is 4 %, by company B is 3 % and by C is 1 %. What is the probability that the randomly purchased product is defect-free?

Produced by company B: $30x+x+30x=100 \implies x=\frac{100}{61}$

Produced by companies A and C: $30x=\frac{3000}{61}$

Defective: $$P(D)=P(A)\cdot P(D|A)+P(B)\cdot P(D|B)+P(C)\cdot P(D|C)$$ $$P(D)=\frac{3000}{61}\cdot 0.04+\frac{100}{61}\cdot 0.03+\frac{3000}{61}\cdot 0.01\;\dot =\;2.5082\%$$

Deffect-free: $$P(\bar D)=1-P(D)\;\dot =\;97.4918\%$$

Could you please confirm, that I understood and solved the problem correctly? Many thanks!

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    $\begingroup$ It's 30% more products (IE 1.3x, 1.3x, x), not 30x more products. $\endgroup$
    – Eric
    Mar 1, 2016 at 18:47

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