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  • Provide solution for RD Sharma maths class 12 chapter Probability exercise 30.6 question 2

Provide solution for RD Sharma maths class 12 chapter Probability exercise 30.6 question 2

Answers (1)

Answer:

 \frac{19}{42}

Hint:

 We use probability formula

Given:

 Purse 1 = 2 silver ; 4 copper coins

Purse 2 = 4 silver ; 3 copper coins

Solution:

Let E1 be the event of selecting purse 1 and then drawing a silver coin from it

Let E2 be the event of selecting purse 2 and then drawing a silver coin from it

Let S be the event of drawing a silver coin

\begin{aligned} &P(E_1)=\frac{1}{2} \qquad ; \qquad P(E_2)=\frac{1}{2}\\ &P\left (\frac{S}{E_1} \right )=\frac{2}{6} \qquad ; \qquad P\left (\frac{S}{E_2} \right )=\frac{4}{7} \end{aligned}

Using total probabilty theorem

\begin{aligned} &\text { required probability }=P(E_1)\times P\left (\frac{S}{E_1} \right )+ P(E_2)\times P\left (\frac{S}{E_2} \right )\\ &=\frac{1}{2}\times \frac{2}{6}+\frac{1}{2}\times \frac{4}{7}\\ &=\frac{1}{2}\left [ \frac{2}{6}+\frac{4}{7} \right ]\\ &=\frac{1}{2}\left [ \frac{1}{3}+\frac{4}{7} \right ]\\ &=\frac{1}{2}\left [ \frac{7+12}{21} \right ]=\frac{19}{42} \end{aligned}

Posted by

Gurleen Kaur

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