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  • Please solve RD Sharma class 12 chapter Probability exercise 30.6 question 13 maths textbook solution

Please solve RD Sharma class 12 chapter Probability exercise 30.6 question 13 maths textbook solution

Answers (1)

Answer:

\frac{17}{400} 

Hint:

 To solve this we find the (B1, B2 and B3) then use total probability

Given:

 E1: 50% Production, E2: 25% Production, E3: 25% Production

Solution:

B1 is the event when E1 produce bulbs

B2 is the event when E2 produce bulbs

B3 is the event when E3 produce bulbs

E event when a defective bulbs is selected

\begin{aligned} &P(B_1)=\frac{1}{2} \qquad ; \qquad P(B_2)=\frac{1}{4} \qquad ; \qquad P(B_3)=\frac{1}{4}\\ &P\left (\frac{E}{B_1} \right )=\frac{4}{100}=\frac{1}{25}\\ &P\left (\frac{E}{B_2} \right )=\frac{4}{100}=\frac{1}{25}\\ &P\left (\frac{E}{B_3} \right )=\frac{5}{100}=\frac{1}{20} \end{aligned}

Using total probability theorem,

\begin{aligned} &P(E)=P(B_1)\times P\left (\frac{E}{B_1} \right )+ P(B_2)\times P\left (\frac{E}{B_2} \right )+P(B_3)\times P\left (\frac{E}{B_3} \right )\\ &P(E)=\frac{1}{2}\times \frac{1}{25}+\frac{1}{4}\times \frac{1}{25}+\frac{1}{4}\times \frac{1}{20}\\ &P(E)=\frac{17}{400} \end{aligned}

Posted by

Gurleen Kaur

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