Provide solution for RD Sharma maths class 12 chapter Probability exercise 30.7 question 26

Answers (1)

Answer:

 \frac{9}{13}

Hint:

 Use Baye’s theorem.

Given:

 It is known that 60%beside in a hostel and 40% don’t reside in hostel. Previous year results report that 30% of student residing in hostel attain. A grade and 20% of ones not residing in hostel attain.

Solution:

Let A denotes A -grade

H denote from hostel

D denote day scholar

\begin{aligned} &P(H)=0.6\\ &P(D)=0.4\\ &P\left ( \frac{A}{H} \right )=0.3\\ &P\left ( \frac{A}{D} \right )=0.2\\ \end{aligned}

Using Baye’s theorem we get

\begin{aligned} &P\left (\frac{H}{A} \right )=\frac{P(H).P\left ( \frac{A}{H} \right )}{P(H)\times P\left ( \frac{A}{H} \right )+P(D)\times P\left ( \frac{A}{D} \right )}\\ &=\frac{{0.3\times 0.6 }}{0.3\times 0.6+0.2\times 0.4}\\ &=\frac{0.18}{0.08}\\ &=\frac{18}{26}\\ &=\frac{9}{13} \end{aligned}

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