COMEDK · Maths · 36. Probability
A certain item is manufactured by 3 factory \(F_{1}, F_{2}\) and \(F_{3}\) with \(30 \%\) of item made in \(F_{1}, 20 \%\) in \(F_{2}\) and \(50 \%\) in \(F_{3}\). It is found that \(2 \%\) of the items produced by \(F_{1} .3 \%\) of the items produced by \(F_{2}\) and \(4 \%\) of the items produced by \(F_{3}\) are defective. Suppose that an items selected at random from the stock is found defective. What is the probability that the item came from \(F_{1}\) ?
- A \(\frac{1}{16}\)
- B \(\frac{1}{8}\)
- C \(\frac{1}{3}\)
- D \(\frac{3}{16}\)
Answer & Solution
Correct Answer
(D) \(\frac{3}{16}\)
Step-by-step Solution
Detailed explanation
Let events \(T_{1}, T_{2}, T_{3}\) be the following \(T_{1}\) : The item is manufactured by factory \(F_{1}\). \(T_{2}\) : The item is manufactured by factory \(F_{2}\). \(T_{3}\) : : The item is manufactured by factory \(F_{3}\). Clearly, \(T_{1}, T_{2}, T_{3}\) are mutually…
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