Get Answers to all your Questions

header-bg qa

Please solve RD Sharma class 12 chapter Probability exercise 30.7 question 37 maths textbook solution

Answers (1)

Answer:

 \frac{12}{13}

Hint:

Use baye’s theorem. 

Given:

 In answering a question on multiple choice tests, students either answers or guess. Assume the student who guess at answer will correct with probability

\frac{1}{4}

Solution:

Let

A = student know answer

B= student guess

C = student answer correctly

We know to find probability that student know answer if he answer is correctly.

\begin{aligned} &P(A)=\frac{3}{4}\\ &P(B)=\frac{1}{4}\\ &P\left ( \frac{C}{A} \right )=1\\ &P\left ( \frac{C}{B} \right )=\frac{1}{4}\\ \end{aligned}

Using Baye’s theorem we get

Required probability

\begin{aligned} &P\left (\frac{A}{C} \right )=\frac{P(A).P\left ( \frac{C}{A} \right )}{P(A)\times P\left ( \frac{C}{A} \right )+P(B)\times P\left ( \frac{C}{B} \right )}\\ &=\frac{{\frac{3}{4}\times 1 }}{\frac{3}{4}\times 1+\frac{1}{4}\times \frac{1}{4}}\\ &=\frac{\frac{1}{4}\times 1}{\frac{1}{4}\left ( \frac{1}{4}+3 \right )}\\ &=\frac{3}{\frac{1}{4}+3}\\ &=\frac{3}{\frac{13}{4}}\\ &=\frac{12}{13} \end{aligned}

Posted by

Gurleen Kaur

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads