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

Please solve RD Sharma Class 12 Chapter 30 Probability Exercise Case Study Based  Question, question 1 sub question (iv) 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:

 First we find,

The probability that an error is committed in processing given that Vinay processed form

i.e. P\left (\frac{V}{E} \right )

Now,

\begin{aligned} &P\left(\frac{V}{E}\right)=\frac{P(V) \cdot P\left(\frac{E}{V}\right)}{P(V) \cdot P\left(\frac{E}{V}\right)+P(S) \cdot P\left(\frac{E}{S}\right)+P(I) \cdot P\left(\frac{E}{I}\right)} \\ &=\frac{50 \% \times 0.06}{50 \% \times 0.06+20 \% \times 0.04+30 \% \times 0.03} \\ &=\frac{\frac{50}{100} \times 0.06}{\frac{50}{100} \times 0.06+\frac{20}{100} \times 0.04+\frac{30}{100} \times 0.03} \\ &=\frac{0.30}{0.30+0.08+0.09} \\ &=\frac{0.30}{0.47} \\ &=\frac{30}{47} \end{aligned}

Now,

Probability form has an error but not processed by Vinay

\begin{aligned} &=1-P\left(\frac{V}{E}\right) \\ &=1-\frac{30}{47} \end{aligned} \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \quad\left[P\left(\frac{V}{E}\right)=\frac{30}{47}\right]

\begin{aligned} &=\frac{47-30}{47} \\ &=\frac{17}{47} \end{aligned}

So, (d) is correct answer

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