A company has two plants A and B to manufacture motorcycles.

Question

A company has two plants $A$ and $B$ to manufacture motorcycles. $$60 \%$$ motorcycles are manufactured at plant $A$ and the remaining are manufactured at plant $$B .80 \%$$ of the motorcycles manufactured at plant $A$ are rated of the standard quality, while $$90 \%$$ of the motorcycles manufactured at plant $B$ are rated of the standard quality. A motorcycle picked up randomly from the total production is found to be of the standard quality. If $p$ is the probability that it was manufactured at plant $B$, then $126 p$ is

Accepted Answer

$$\begin{aligned}
& P(\text { standard automobile from } A)=\frac{6}{10} \times \frac{8}{10}=\frac{12}{25} \
& P(\text { standard automobile from } B)=\frac{4}{10} \times \frac{9}{10}=\frac{9}{25}
\end{aligned}$$

$$\begin{aligned}
& \text { Required Probability } \frac{\frac{9}{25}}{\frac{12}{25}+\frac{9}{25}} \
& P=\frac{9}{21}=\frac{3}{7}
\end{aligned}$$

So, $$126 P=126 \times \frac{3}{7}=54$$

Solutions · 1