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An article manufactured by a company consists of two parts A and B. In the process of manufacture 13 out of 104 parts of A and 5 out of 100 parts of B may be defective then the probability that the assembled product is not defective is

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$\frac{28}{160}$

$\frac{33}{160}$

$\frac{128}{160}$

$\frac{133}{160}$

answer is D.

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Detailed Solution

A=article A defective items

B=article B defective items

$\begin{array}{rcl} P (A) & = & \frac{13}{104} P (B) = \frac{5}{100} \end{array}$

$\begin{array}{rcl} P (A \cap B) & = & P (A) \cdot P (B) \end{array}$

$\begin{array}{rcl} = & \frac{91}{104} \times \frac{95}{100} = \frac{133}{160} \end{array}$

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