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  • Please solve RD Sharma class 12 chapter Probability exercise 30.7 question 17 maths textbook solution

Please solve RD Sharma class 12 chapter Probability exercise 30.7 question 17 maths textbook solution

Answers (1)

Answer:

 \frac{3}{7}

Hint:

 Use Bayes theorem.

Given:

 The first plant manufacture 60% of bicycle and second plant 40% out of that 80% of bicycle are rated of standard quality at first plant and 90% of standard quality at second plant.

Solution:

E1 be event of cycle is from first plant

E2 be event of second plant

A be event the cycle is standard

\begin{aligned} &P(E_1)=0.6\\ &P(E_2)=0.4\\ &P\left ( \frac{A}{E_1} \right )=0.8\\ &P\left ( \frac{A}{E_2} \right )=0.9\\ \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{0.4\times 0.9}{0.6\times 0.8+0.4\times 0.9}\\ &=\frac{0.36}{0.84}\\ &=\frac{36}{84}\\ &=\frac{9}{21}=\frac{3}{7} \end{aligned}

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Gurleen Kaur

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