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  • Need solution for RD Sharma maths class 12 chapter Probability exercise 30.7 question 7

Need solution for RD Sharma maths class 12 chapter Probability exercise 30.7 question 7

Answers (1)

Answer:

 \frac{2}{3}

Hint:

Use Baye’s theorem. 

Given:

 Suppose 5 men out of 100 and 25 women out of 1000 are good orator. An orator chose at random. Find the probability that make person is selected. Assume equal number of men and women.

Solution:

Let A, E1and E2  two events that person is good orator.

Thus

\begin{aligned} &P(E_1)=\frac{1}{2}\\ &P(E_2)=\frac{1}{2}\\ &P\left ( \frac{A}{E_1} \right )=\frac{5}{100}\\ &P\left ( \frac{A}{E_2} \right )=\frac{25}{1000}\\ \end{aligned}

Using Baye’s theorem we get

\begin{aligned} &P\left (\frac{E_1}{A} \right )=\frac{P(E_2).P\left ( \frac{A}{E_1} \right )}{P(E_1)\times P\left ( \frac{A}{E_1} \right )+P(E_2)\times P\left ( \frac{A}{E_2} \right )}\\ &P\left (\frac{E_2}{A} \right )=\frac{\frac{1}{2}\times \frac{5}{100}}{\frac{1}{2}\times \frac{5}{100}+\frac{1}{2}\times \frac{25}{1000}}\\ &=\frac{1}{1+\frac{1}{2}}\\ &=\frac{2}{3} \end{aligned}

Posted by

Gurleen Kaur

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