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  • Need solution for RD Sharma maths class 12 chapter Probability exercise 30.7 question 35

Need solution for RD Sharma maths class 12 chapter Probability exercise 30.7 question 35

Answers (1)

Answer:

 \frac{3}{13}

Hint:

 Use baye’s theorem.

Given:

 A is known to speak with 3 time out of 5 time. He throws a die and report that is one. Find the probability that actually one.

Solution:

Let  A, E1 and E2  denote the events that the man reports the appearance of 1 on throwing a die, 1 occur and 1 does not occur respectively.

\begin{aligned} &P(E_1)=\frac{1}{6}\\ &P(E_2)=\frac{5}{6}\\ \end{aligned}

Now,

\begin{aligned} &P\left ( \frac{A}{E_1} \right )=\frac{3}{5}\\ &P\left ( \frac{A}{E_2} \right )=\frac{2}{5}\\ \end{aligned}

Using Baye’s theorem we get

Required probability

\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}{6}\times \frac{3}{5} }}{\frac{1}{6}\times \frac{3}{5}+\frac{5}{6}\times \frac{2}{5}}\\ &=\frac{3}{3+10}\\ &=\frac{3}{13} \end{aligned}

 

Posted by

Gurleen Kaur

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