In a bolt factory, machines A, B and C manufacture respectively [20 %, 30 %] and [50 %] of…

Question

In a bolt factory, machines $A, B$ and $C$ manufacture respectively $$20 \%, 30 \%$$ and $$50 \%$$ of the total bolts. Of their output 3, 4 and 2 percent are respectively defective bolts. A bolt is drawn at random from the product. If t...

Accepted Answer

Given : $P(A)=\frac{20}{100}=\frac{2}{10}$

$P(B)=\frac{30}{100}=\frac{3}{10}$

$P(C)=\frac{50}{100}=\frac{5}{10}$

Let $E	o$ Event that the bolt is defective.

$P(E/A)=\frac{3}{100},$

$P(\frac{E}{B})=\frac{4}{100},P(\frac{E}{C})=\frac{2}{100}$

So, $P(C/E)$

$\begin{gathered} =\frac{P(\frac{E}{C})	imes P(C)}{P(\frac{E}{A})	imes P(A)+P(\frac{E}{B})	imes P(B)+P(\frac{E}{C})	imes P(C)} \ =\frac{\frac{5}{10}	imes \frac{2}{100}}{\frac{3}{100}	imes \frac{2}{10}+\frac{4}{100}	imes \frac{3}{10}+\frac{2}{100}	imes \frac{5}{10}} \ =\frac{10}{6+12+10}=\frac{10}{28}=\frac{5}{14} \end{gathered}$

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