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  • Please solve RD Sharma Class 12 Chapter 30 Probability Exercise Case Study Based  Question, question 1 sub question (v) Maths textbook solution.

Please solve RD Sharma Class 12 Chapter 30 Probability Exercise Case Study Based  Question, question 1 sub question (v) Maths textbook solution.

Answers (1)

Answer:

            (d)

Hint:

            You must know rules of conditional probability

Given:

            Vinay process 50% forms, Sonia process 20% and Iqbal process 30%. Vinay has an error of 0.06, Sonia has error rate 0.04 and Iqbal has error rate of 0.03

Solution:

Now

E1 = Vinay

E2 = Sonia

E3 = Iqbal

Now

\begin{aligned} &\sum_{i=1}^{3} P\left(\frac{E_{i}}{A}\right)=P\left(\frac{E_{1}}{A}\right)+P\left(\frac{E_{2}}{A}\right)+P\left(\frac{E_{3}}{A}\right) \\ &=\frac{P\left(E_{1}\right) \cdot P\left(\frac{A}{E_{1}}\right)}{P\left(E_{1}\right) \cdot P\left(\frac{A}{E_{1}}\right)+P\left(E_{2}\right) \cdot P\left(\frac{A}{E_{2}}\right)+P\left(E_{3}\right) P\left(\frac{A}{E_{3}}\right)} \\ &+\frac{P\left(E_{2}\right) \cdot P\left(\frac{A}{E_{2}}\right)}{P\left(E_{1}\right) \cdot P\left(\frac{A}{E_{1}}\right)+P\left(E_{2}\right) \cdot P\left(\frac{A}{E_{2}}\right)+P\left(E_{3}\right) P\left(\frac{A}{E_{3}}\right)} \\ &+\frac{P\left(E_{3}\right) \cdot P\left(\frac{A}{E_{3}}\right)}{P\left(E_{1}\right) \cdot P\left(\frac{A}{E_{1}}\right)+P\left(E_{2}\right) \cdot P\left(\frac{A}{E_{2}}\right)+P\left(E_{3}\right) P\left(\frac{A}{E_{3}}\right)} \end{aligned}

\begin{aligned} &=\frac{\left(P\left(E_{1}\right) \cdot P\left(\frac{A}{E_{1}}\right)+P\left(E_{2}\right) \cdot P\left(\frac{A}{E_{2}}\right)+P\left(E_{3}\right) \cdot P\left(\frac{A}{E_{3}}\right)\right)}{\left(P\left(E_{1}\right) \cdot P\left(\frac{A}{E_{1}}\right)+P\left(E_{2}\right) \cdot P\left(\frac{A}{E_{2}}\right)+P\left(E_{3}\right) \cdot P\left(\frac{A}{E_{3}}\right)\right)} \\ \end{aligned}

=1

So, (d) is correct answer

Posted by

infoexpert24

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