Question

Let A consists of $3$G and $2$D articles. Let B consists of $4$G and $1$D article. A new lot C is formed by taking $3$ article from A an $2$ from B. The probability that an article chosen at random from C is defective, is?

• A. $\frac{1}{3}$
• B. $\frac{2}{5}$
• C. $\frac{8}{25}$
• D. None

Answer 1

The correct option is C $\frac{8}{25}$

Let $A$ be the event article chosen from $A$

$\therefore$ $P\left(A\right)=\frac{3}{3+2}=\frac{3}{5}$

Let $B$ be the event article chosen from $B$

$\therefore$ $P\left(A\right)=\frac{2}{4+1}=\frac{2}{5}$

$\Rightarrow$ Probability of defective chosen from $A=P\left(\frac{D}{A}\right)=\frac{2}{5}$

$\Rightarrow$ Probability of defective chosen from $B=P\left(\frac{D}{B}\right)=\frac{1}{5}$

$P\left(D\right)=P\left(A\right)\times P\left(\frac{D}{A}\right)+P\left(B\right)\times \left(\frac{D}{B}\right)$

$=\frac{3}{5}\times \frac{2}{5}+\frac{2}{5}\times \frac{1}{5}$

$=\frac{6}{25}+\frac{2}{25}$

$=\frac{8}{25}$