Question

A car manufacturing factory has two plants $X$ and $Y$. Plant $X$ manufactures $70\%$ of cars and plant $Y$ manufactures $30\%$ of cars. $80\%$ of cars at plant $X$ and $90\%$ of cars at plant $Y$ are rated as standard quality. $A$ car is chosen at random and is found to be of standard quality. The probability that it has come from plant $X$ is

• A. $\frac{56}{73}$
• B. $\frac{56}{84}$
• C. $\frac{56}{83}$
• D. $\frac{56}{79}$

Answer 1

Answer: (C)

$=\frac{\frac{70}{100}\times \frac{80}{100}}{\frac{70}{100}\times \frac{80}{100}+\frac{90}{100}\times \frac{30}{100}}$
$=\frac{56}{83}$