Q48 / 90 · JEE Main 2024 (06 Apr Shift 1) · Mathematics

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

  • Correct answer
    A
    54
  • B
    66
  • C
    64
  • D
    56

Solution

$\begin{array}{|l|c|c|} \hline & \text{A} & \text{B} \\ \hline \text{Manufactured} & 60 \% & 40 \% \\ \hline \text{Standard quality} & 80 \% & 90 \% \\ \hline \end{array}$ $\mathrm{P}$ (Manufactured at $\mathrm{B} /$ found standard quality $)=$ ? A : Found S.Q B : Manufacture B $\mathrm{C}$ : Manufacture A $\begin{aligned} & P\left(E_1\right)=\frac{40}{100} \\ & P\left(E_2\right)=\frac{60}{100} \\ & P\left(A / E_1\right)=\frac{90}{100} \\ & P\left(A / E_2\right)=\frac{80}{100} \\ & \because P\left(E_1 / A\right)=\frac{P\left(A / E_1\right) P\left(E_1\right)}{P\left(A / E_1\right) P\left(E_1\right)+P\left(A / E_2\right) P\left(E_2\right)}=\frac{3}{7} \\ & \therefore 126 P=54 \end{aligned}$

Hence, the correct answer is option: 'A'.

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