A company manufactures scooters at two plants, $A$ and B. plant A produces $80 \%$ and plant B produces $20 \%$ of the total product. $85 \%$ of the scooters produced at pant $A$ and $65 \%$ of the scooters produced at plant $B$ are of standard quality. A scooter produced by the company is selected at random, and it is found to be of standard quality. What is the probability that it was manufactured at plant A?

Home » A company manufactures scooters at two plants, and B. plant A produces and plant B produces of the total product. of the scooters produced at pant and of the scooters produced at plant are of standard quality. A scooter produced by the company is selected at random, and it is found to be of standard quality. What is the probability that it was manufactured at plant A?

A company manufactures scooters at two plants, $A$ and B. plant A produces $80 \%$ and plant B produces $20 \%$ of the total product. $85 \%$ of the scooters produced at pant $A$ and $65 \%$ of the scooters produced at plant $B$ are of standard quality. A scooter produced by the company is selected at random, and it is found to be of standard quality. What is the probability that it was manufactured at plant A?

Let S : Standard quality
We want to find $\mathrm{P}(\mathrm{A} \mid \mathrm{S})$ , i.e. probability that selected standard scooter is from
plant A
$\mathrm{P}(\mathrm{A} \mid \mathrm{S})=\frac{\mathrm{P}(\mathrm{A}) \cdot \mathrm{P}(\mathrm{A} \mid \mathrm{S})}{\mathrm{P}(\mathrm{A}) \cdot \mathrm{P}(\mathrm{S} \mid \mathrm{A})+\mathrm{P}(\mathrm{B}) \cdot \mathrm{P}(\mathrm{S} \mid \mathrm{B})}$
Where, $\mathrm{P}(\mathrm{A})=$ probability that scooter is from $\mathrm{A}=\frac{80}{100}$
$P(B)=$ probability that scooter is from $B=\frac{20}{100}$
$\mathrm{P}(\mathrm{S} \mid \mathrm{A})=$ probability that standard scooter from $\mathrm{A}=\frac{85}{100}$
$P(S \mid B)=$ probability that standard scooter from $B=\frac{65}{100}$
$\begin{array}{l} P(A \mid S)=\frac{(80)(85)}{(80)(85)+(20)(65)} \\ =\frac{6800}{6800+1300}=\frac{68}{81} \end{array}$
Therefore, the probability of selected standard scooter is from plant $A$ is $\frac{68}{81}$