A bolt is manufactured by 3 machines a, b and
c. Machine a turn out twice as many items as b, and machines b and c produce equal number of items. 2% of bolts produced by a and b are defective and 4% of bolts produced by c are defective. All bolts are put into 1 stock pile and 1 is chosen from this pile. What is The probability that it is defective
Answers
Answer:
Step-by-step explanation:
Let A =the event in which item has been produced by machine A. and so on.
D =The event of the item being defective.
P(A)= 1/2 ,P(B)=1/4
P(D/A)=P(An item is defective, given that A has produced it)
=2/100 =P(D/B)
P(D/C) =4/100
By theorem of total productivity,
P(D)= P(A)* P(D/A)+P(B)*(D/B)+P(C)*(D/C)
=1/2 x 2/100 + 1/4 x 2/100 + 1/4 x 4/100
=1/40
Probability of defective bolt is 0.025 or 2.5 %
Given:
A bolt is manufactured by 3 machines a, b and c.
Machine a produces twice of Machine b and c
Machine a and b produce 2 % defectives
Machine c produces 4 % defectives
All bolts are put into 1 stock pile
1 is chosen from this pile
To Find:
The probability that bolt is defective
Solution:
- Probability of an event = n(E)/n(S)
- n(E) = number of possible outcome of event
- n(S) = number of possible sample space outcome
Step 1:
Assume that machine b and c produce 100 items each.
Then machine a produce 2 * 100 = 200 items
Step 2:
Find defective items produced by each machine
Defective by machine a = (2/100)200 = 4
Defective by machine b = (2/100)100 = 2
Defective by machine c = (4/100)100 = 4
Step 3:
Count total produced and total defectives
Total Produced = 200 + 100 + 100 = 400
Total Defectives = 4 +2 + 4 = 10
Step 4:
Calculate the probability
Probability = 10/400 = 0.025 = 2.5 %
Probability of bolt being defective is 0.025 or 2.5 %