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In-my-house-there-is-250-laptops-40-are-new-100-are-recent-and-the-others-are-old-A-statistic-showed-that-4-of-new-laptops-are-faulty-12-of-recent-ones-are-faulty-and-25-of-old-ones-are-fau




Question Number 134751 by mathocean1 last updated on 06/Mar/21
 In my house, there is 250 laptops:   40 are new, 100 are recent and the   others are old. A statistic showed that  4% of new laptops are faulty, 12% of  recent ones are faulty and 25% of old  ones are faulty.  Calculate the probability that 1 laptop be  new , knowing that it is faulty.
$$\:{In}\:{my}\:{house},\:{there}\:{is}\:\mathrm{250}\:{laptops}:\: \\ $$$$\mathrm{40}\:{are}\:{new},\:\mathrm{100}\:{are}\:{recent}\:{and}\:{the}\: \\ $$$${others}\:{are}\:{old}.\:{A}\:{statistic}\:{showed}\:{that} \\ $$$$\mathrm{4\%}\:{of}\:{new}\:{laptops}\:{are}\:{faulty},\:\mathrm{12\%}\:{of} \\ $$$${recent}\:{ones}\:{are}\:{faulty}\:{and}\:\mathrm{25\%}\:{of}\:{old} \\ $$$${ones}\:{are}\:{faulty}. \\ $$$${Calculate}\:{the}\:{probability}\:{that}\:\mathrm{1}\:{laptop}\:{be} \\ $$$${new}\:,\:{knowing}\:{that}\:{it}\:{is}\:{faulty}. \\ $$
Answered by EDWIN88 last updated on 07/Mar/21
p(A)=((0.04)/(0.04+0.12+0.25)) = ((0.04)/(0.41))= (4/(41))
$$\mathrm{p}\left(\mathrm{A}\right)=\frac{\mathrm{0}.\mathrm{04}}{\mathrm{0}.\mathrm{04}+\mathrm{0}.\mathrm{12}+\mathrm{0}.\mathrm{25}}\:=\:\frac{\mathrm{0}.\mathrm{04}}{\mathrm{0}.\mathrm{41}}=\:\frac{\mathrm{4}}{\mathrm{41}} \\ $$$$ \\ $$

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