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  • Provide solution for RD Sharma maths class 12 chapter Probability exercise 30.7 question 2

Provide solution for RD Sharma maths class 12 chapter Probability exercise 30.7 question 2

Answers (1)

Answer:

 \frac{25}{52}

Hint:

 Use baye’s theorem.

Given:

 A bag A contained 2 white and 3 red ball and a bag B contain 5 red and 4 white ball one ball drawn at random from one of bag is found red. What is probability that it was drawn from bag B?.

Solution:

The event selecting red ball denoted by R.

The event selected by bag A denoted by A.

The event selected by bag B denoted by B.

Bag A = 2 white and 3red ball.

Bag B = 4 white and 5 red ball.

\begin{aligned} &P(A)=P(B)=\frac{1}{2}\\ &P\left ( \frac{R}{A} \right )=\frac{3}{5}\\ &P\left ( \frac{R}{B} \right )=\frac{5}{9}\\ \end{aligned}

Using Baye’s theorem

\begin{aligned} &P\left ( \frac{B}{R} \right )=\frac{P\left ( \frac{R}{A} \right ).P(B)}{P(R)} \\ &=\frac{P\left ( \frac{R}{A} \right ).P(B)}{P\left ( \frac{R}{A} \right ).P(A)+P\left ( \frac{R}{B} \right ).P(B)} \\ &=\frac{\frac{5}{9}.\frac{1}{2}}{\frac{3}{5}\times \frac{1}{2}+\frac{5}{9}\times \frac{1}{2}}\\ &=\frac{25}{52} \end{aligned}

Posted by

Gurleen Kaur

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