Question 6 - Case Based Questions (MCQ) - Chapter 13 Class 12 Probability

Last updated at March 16, 2023 by Teachoo

Question

A factory has 3 machines X, Y and Z, producing 1000, 2000 and 3000 bolts per day respectively. The machine XΒ produces 1% defective bolts, Y produces 1.5% defective bolts and Z produces 2% defective bolts. At the end of theΒ day, a bolt is drawn at random and it is found to be defective.Β

Let,

Β E1 = event of drawing a bolt produced by machine X.Β

Β E2 = event of drawing a bolt produced by machine Y.Β

Β E3 = event of drawing a bolt produced by machine Z.Β

Β E = event of drawing a defective bolt.Β

Based on the above information answer the following questions:

Β

Question 1

What is the value of P(E2)?

(A) 1/6Β Β

(B) 1/3

(C) 1/2 Β Β Β

(D) 1/4

Question 2

Find the value of P(E|E1)?

(A) 1/100Β

(B) 3/200

(C) 1/50 Β Β

(D) 1/10

Question 3

Find the value of P(E | E2)?

(A) 1/100Β

(B) 3/200

(C) 1/50Β Β

(D) 1/10

Question 4

Find the value of P(E|E3)?

(A) 1/100Β

(B) 3/200

(C) 1/50Β Β

(D) 1/10

Question 5

What is the probability that the drawn bolt has been produced by the machine X?

Question A factory has 3 machines X, Y and Z, producing 1000, 2000 and 3000 bolts per day respectively. The machine X produces 1% defective bolts, Y produces 1.5% defective bolts and Z produces 2% defective bolts. At the end of the day, a bolt is drawn at random and it is found to be defective. Let, E1 = event of drawing a bolt produced by machine X. E2 = event of drawing a bolt produced by machine Y. E3 = event of drawing a bolt produced by machine Z. E = event of drawing a defective bolt. Based on the above information answer the following questions:Question 1 What is the value of P(E2)? (A) 1/6 (B) 1/3 (C) 1/2 (D) 1/4 Now,
P(E2) = (ππ’ππππ ππ ππππ‘π πππππ’πππ ππ¦ πππβπππ π)/(πππ‘ππ ππ’ππππ ππ ππππ‘π πππππ’πππ ππ¦ πππ 3 πππβππππ )
Number of bolts produced by machine Y = 2000
Total number of defective bolts = 1000 + 2000 + 3000
= 6000
Thus,
P(E2) = 2000/6000= π/π
So, the correct answer is (B)
Question 2 Find the value of P(E|E1)? (A) 1/100 (B) 3/200 (C) 1/50 (D) 1/10 P(E | E1) = P(defective bolt | produced by machine X)
= P( defective bolt is produced by machine X)
Since Machine X produces 1% defective bolts
= 1%
= π/πππ
So, the correct answer is (a)
Question 3 Find the value of P(E | E2)? (A) 1/100 (B) 3/200 (C) 1/50 (D) 1/10 P(E | E1) = P(defective bolt | produced by machine Y)
= P( defective bolt is produced by machine Y)
Since Machine Y produces 1.5% defective bolts
= 1.5 %
= 1.5/100
= π/πππ
So, the correct answer is (B)
Question 4 Find the value of P(E|E3)? (A) 1/100 (B) 3/200 (C) 1/50 (D) 1/10 P(E | E3) = P(defective bolt | produced by machine Z)
= P( defective bolt is produced by machine Z)
Since Machine Z produces 2% defective bolts
= 2 %
= π/πππ
= π/ππ
So, the correct answer is (c)
Question 5 What is the probability that the drawn bolt has been produced by the machine X? (A) 1/10 (B) 3/200 (C) 1/20 (D) 1/30 We need to find
Probability that the drawn defective bolt is produced by machine X
i.e. P(π¬_π "|E")
So, "P(" π¬_π "|E) = " (π(πΈ_1 ). π(πΈ|πΈ_1))/(π(πΈ_1 ). π(πΈ|πΈ_1 ) + π(πΈ_2 ). π(πΈ|πΈ_2 )+π(πΈ_3 ). π(πΈβ€| πΈ_3) )
"P(" π¬_π ")" = Probability
that the bolt is made
by machine X
= 1000/6000 = π/π
π·("E|" π¬_π)
This is calculated in
Question 2
π("E|" πΈ_1) = π/πππ
"P(" π¬_π ")" = Probability
that the bolt is made
by machine Y
= 2000/6000 = π/π
π·("E|" π¬_π)
This is calculated in
Question 3
π("E|" πΈ_2) = π/πππ
"P(" π¬_π ")" = Probability
that the bolt is made
by machine Z
= 3000/6000 = π/π
π·("E|" π¬_π)
This is calculated in
Question 4
π("E|" πΈ_3) = π/ππ
Putting values in formula, "P(" πΈ_1 "|E) = " (1/6 Γ 1/100)/(1/6 Γ 1/100 + 1/3 Γ 3/200 + 1/2 Γ 1/50)
= ( 1/600)/(1/600 + 1/200 + 1/100)
= ( 1/600)/((1 + 3 + 6)/600 )
= ( 1/600)/(10/600 )
Putting values in formula,
"P(" πΈ_1 "|E) = " (1/6 Γ 1/100)/(1/6 Γ 1/100 + 1/3 Γ 3/200 + 1/2 Γ 1/50)
= ( 1/600)/(1/600 + 1/200 + 1/100)
= ( 1/600)/((1 + 3 + 6)/600 )
= ( 1/600)/(10/600 )
= 1/600Γ600/10
= π/ππ
So, the correct answer is (a)

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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