Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
350 views
in Probability by (45 points)
A factory has two Machines -I and II. Machine-I produces \( 60 \% \) of items and Machine-II produces \( 40 \% \) of the items of the total output. Further \( 2 \% \) of the items produced by Machine-I are defective whereas \( 4 \% \) produced by Machine-II are defective. If an item is drawn at random what is the probability that it is defective?
by (45 points)
Hiii answer please

Please log in or register to answer this question.

2 Answers

+1 vote
by (45 points)
Let A₁, be the event that the items are produced by Machine - I, A, be the event that the items are produced by Machine - II. Let B be the event of drawing a defective item. 60 100 Given P(A₁) 2 100 P (B/A₁) 40 P(A₂) P (B/A₂) 100 100 = We have to find the total probability of event B. Since A A, are mutually exclusive and exhaustive events, we have P(B) P(A₁).P(B/A₂)+P (A₂). P(B/A₂) P(B) 60/100 2/100 40/100 4/100 -X + P(B) 120/10000 160/10000 280/10000
  = P(B) = 0.028
+1 vote
by (18.1k points)

Let A1, be the event that the items are produced by Machine - I, A, be the event that the items are produced by Machine - II.

Given P(A1) = 60/100 = 3/5

P(A2) = 40/100 = 2/5

P(B | A1) = 2/100 = 1/50

P(B | A2) = 4/100 = 1/25.

We have to find total probability of event B. Since, A1 and A are mutually exhaustive events.

P(B) = P(A1) P(B | A1) + P(A2) P(B | A2)

= 3/5 x 1/50 + 2/5 x 1/25

= 1/125 (3/2 + 2)

= 1/125 x 7/2 = 7/250 = 28/1000 = 0.028

⇒ P(B) = 0.028

∴ The probability that item is defective is 0.028.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...