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

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) (56/73) (B) (56/84) (C) (56/83) (D) (56/79)

Tardigrade Admin · Accepted Answer

=((70/100) × (80/100)/(70)100 × (80)100+(90/100) × (30/100) =(56/83)

$\frac{56}{73}$

$\frac{56}{84}$

$\frac{56}{83}$

$\frac{56}{79}$

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

7356​

8456​

8356​

7956​

=10070​×10080​+10090​×10030​10070​×10080​​ =8356​

$\frac{56}{73}$

$\frac{56}{84}$

$\frac{56}{83}$

$\frac{56}{79}$

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