Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Provide solution for RD Sharma maths class 12 chapter Probability exercise 30.7 question 10

Provide solution for RD Sharma maths class 12 chapter Probability exercise 30.7 question 10

Answers (1)

Answer:

 0.1

Hint:

 Use Baye’s theorem.

Given:

 A factor has three machines X, Y, Z producing 1000, 2000, 3000, bolts per day respectively. The machine X produce 1% defective bolts, Y produce 1.5% defective and Z produce 2% defective bolt.

Solution:

Let E1,E2,E3 denote the event that machine X produce bolts, machine Y produce bolts and 2 produce bolt.

Let A be event that bolt is defective.

Total bolt = 1000 + 2000 + 3000 = 6000

\begin{aligned} &P(E_1)=\frac{1000}{6000}=\frac{1}{6}\\ &P(E_2)=\frac{2000}{6000}=\frac{1}{3}\\ &P(E_3)=\frac{3000}{6000}=\frac{1}{2}\\ &P\left ( \frac{A}{E_1} \right )=1%=\frac{1}{100}\\ &P\left ( \frac{A}{E_2} \right )=1.5%=\frac{15}{1000}\\ &P\left ( \frac{A}{E_3} \right )=2%=\frac{2}{100}\\ \end{aligned}

Using Baye’s theorem we get

\begin{aligned} &P\left (\frac{E_2}{A} \right )=\frac{P(E_2).P\left ( \frac{A}{E_2} \right )}{P(E_1)\times P\left ( \frac{A}{E_1} \right )+P(E_2)\times P\left ( \frac{A}{E_2} \right )+P(E_3)\times P\left ( \frac{A}{E_3} \right )}\\ &=\frac{{\frac{1}{6}\times \frac{1}{100} }}{\frac{1}{6}\times \frac{1}{100}+\frac{1}{3}\times \frac{15}{1000}+\frac{1}{2}\times \frac{2}{100}}\\ &=\frac{\frac{1}{6}}{\frac{1}{6}+\frac{1}{2}+1}\\ &=\frac{1}{6}\times \frac{1+3+6}{6}\\ &=\frac{1}{10} \end{aligned}

Posted by

Gurleen Kaur

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE Board exams twice a year from 2025, no plan for semesters: MoE
anam-khan

CBSE Class 12 board exams 2025 to have 50% competency-based questions; no change in 10th
anam-khan

CBSE Class 12 board exams 2024 over; expected result date, trends of last 10 years

Latest Question