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  • Need solution for RD Sharma Maths Class 12 Chapter 30 Probability Exercise Case Study Based  Question, question 5 sub question (iii).

Need solution for RD Sharma Maths Class 12 Chapter 30 Probability Exercise Case Study Based  Question, question 5 sub question (iii).

Answers (1)

Answer:

            (a)

Hint:

            You must know rules of finding probability

Given:

            Machine A produce 1% defective item, B produce 5%, C produce 7%. Operator A on job for 50% of time B on job for 30% and C on job for 20%

Solution:

A= Event that item produced by operator A

B= Item produced by operator B

C= Item produced by operator C

D= Item produced is defective

\begin{aligned} &P(A)=0.5, P(B)=0.3, P(C)=0.2 \\ &P\left(\frac{D}{A}\right)=0.01, P\left(\frac{D}{B}\right)=0.05, P\left(\frac{D}{C}\right)=0.07 \end{aligned}

A defective item is produced, probability that it was produced by A,

Using Baye’s theorem

\begin{aligned} &P\left(\frac{A}{D}\right)=\frac{P(A) \cdot P\left(\frac{D}{A}\right)}{P(A) \cdot P\left(\frac{D}{A}\right)+P(B) \cdot P\left(\frac{D}{B}\right)+P(C) \cdot P\left(\frac{D}{C}\right)} \\ &=\frac{0.5 \times 0.01}{0.5 \times 0.01+0.3 \times 0.05+0.2 \times 0.07} \\ &=\frac{0.005}{0.005+0.015+0.014} \\ &=\frac{0.005}{0.034} \\ &=\frac{5}{34} \end{aligned}

So, (a) is correct answer

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