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  • Provide solution for RD Sharma maths class 12 chapter Probability exercise 30.7 question 22

Provide solution for RD Sharma maths class 12 chapter Probability exercise 30.7 question 22

Answers (1)

Answer:

 \frac{3}{11}

Hint:

 Use Baye’s theorem.

Given:

 In certain college 4% of boy and 1% of girl are taller than 1.75 meter. Furthermore 60% of student in colleges are girl. A student selected at garden from college is found be taller 1.75 meter.

Solution:

Let E1 and E2  denote the selected student is a girl and selected student is a boy.

A denoted the student is 1.75m tall.

\begin{aligned} &P(E_1)=\frac{60}{100}\\ &P(E_2)=\frac{40}{100}\\ &P\left ( \frac{A}{E_1} \right )=\frac{1}{100}\\ &P\left ( \frac{A}{E_2} \right )=\frac{4}{100}\\ \end{aligned}

Using Baye’s theorem we get

\begin{aligned} &P\left (\frac{E_1}{A} \right )=\frac{P(E_1).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 )}\\ &=\frac{{\frac{60}{100}\times \frac{1}{100} }}{\frac{60}{100}\times \frac{1}{100}+\frac{40}{100}\times \frac{4}{100}}\\ &=\frac{6}{6+16}\\ &=\frac{6}{22}\\ &=\frac{3}{11} \end{aligned}

Posted by

Gurleen Kaur

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