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

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

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