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  • Provide solution for RD Sharma maths class 12 chapter Probability exercise 30.7 question 30

Provide solution for RD Sharma maths class 12 chapter Probability exercise 30.7 question 30

Answers (1)

Answer:

 \frac{81}{85}

Hint:

Use Baye’s theorem. 

Given:

 If machine is correctly set up it produce 90% acceptable item. If it incorrectly set up the produce 40% acceptable item. Past experience show 80% of setup is correctly done. If after certain set up the machine produce 2 acceptance items.

Solution:

Let A be event that machine produce 2 acceptable item.

E1  Represents event of correct setup.

E2  Represents event of incorrect setup.

\begin{aligned} &P(E_1)=0.8\\ &P(E_2)=0.2\\ &P\left ( \frac{A}{E_1} \right )=0.9\times 0.9\\ &P\left ( \frac{A}{E_2} \right )=0.4\times 0.4\\ \end{aligned}

Using Baye’s theorem we get

\begin{aligned} &P\left (\frac{E_2}{A} \right )=\frac{P(E_2).P\left ( \frac{A}{E_2} \right )}{P(E_1)\times P\left ( \frac{A}{E_1} \right )+P(E_2)\times P\left ( \frac{A}{E_2} \right )}\\ &=\frac{{\frac{8}{10}\times \frac{81}{100} }}{\frac{8}{10}\times \frac{81}{100}+\frac{2}{10}\times \frac{16}{100}}\\ &=\frac{648}{680}\\ &=\frac{81}{85} \end{aligned}

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Gurleen Kaur

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