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ProbabilityHard JEE math MCQ

A computer producing factory has only two plants $T_{1}$ and $T_{2}$. Plant $T_{1}$ produces $20 \%$ and plant $T_{2}$ produces $80 \%$ of the total computers produced. $7 \%$ of computers produced in the factory turn out to be defective. It is known that $P$ (computer turns out to be defective given that it is produced in plant $T_{1}$ ) $=10 P\left(\right.$ computer turns out to be defective given that it is produced in plant $\left.T_{2}\right)$, where $P(E)$ denotes the probability of an event $E$. A computer produced in the factory is randomly selected and it does not turn out to be defective. Then the probability that it is produced in plant $T_{2}$ is
  1. A. $\frac{36}{73}$
  2. B. $\frac{47}{79}$
  3. C. $\frac{78}{93}$
  4. D. $\frac{75}{83}$

Solution

The correct option is **C**.

MATH

hardPYQ Reworded
Question
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A computer producing factory has only two plants T1T_{1} and T2T_{2}. Plant T1T_{1} produces 20%20 \% and plant T2T_{2} produces 80%80 \% of the total computers produced. 7%7 \% of computers produced in the factory turn out to be defective. It is known that PP (computer turns out to be defective given that it is produced in plant T1T_{1} ) =10P(=10 P\left(\right. computer turns out to be defective given that it is produced in plant T2)\left.T_{2}\right), where P(E)P(E) denotes the probability of an event EE. A computer produced in the factory is randomly selected and it does not turn out to be defective. Then the probability that it is produced in plant T2T_{2} is
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Probability — Hard JEE Mathematics MCQ | MyGoalPrep