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  • Please solve RD Sharma class 12 chapter Probability exercise 30.7 question 21 maths textbook solution

Please solve RD Sharma class 12 chapter Probability exercise 30.7 question 21 maths textbook solution

Answers (1)

Answer:

 \frac{1}{5}

Hint:

 Use Baye’s theorem.

Given:

 A bag contain 1 white and 6 red ball, and second bag contain 4 white 3 red. One of the bags is pick at random and ball is randomly drawn from college to white in color.

Solution:

Let E1, E2,E3 be event

E1 = E2 = Selection of bag,

A=The white ball drawn random

\begin{aligned} &P(E_1)=\frac{1}{2}\\ &P(E_2)=\frac{1}{2}\\ &P\left ( \frac{A}{E_1} \right )=\frac{1}{7}\\ &P\left ( \frac{A}{E_2} \right )=\frac{4}{7}\\ \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{1}{2}\times \frac{1}{7} }}{\frac{1}{2}\times \frac{1}{7}+\frac{1}{2}\times \frac{4}{7}}\\ &=\frac{1}{1+4}\\ &=\frac{1}{5} \end{aligned}

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Gurleen Kaur

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