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A bolt is manufactured by 3 machines A, B and C. Machine A turns out twice as many items as B and machines B and C produce an 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 put into 1 stockpile and 1 is chosen from this pile. What is the probability that it is defective?
- a)0.075
- b)0.025
- c)0.15
- d)0.20
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
A bolt is manufactured by 3 machines A, B and C. Machine A turns out t...
To solve this problem, let's break it down step by step:
1. Determine the production ratios:
- Machine A produces twice as many items as Machine B.
- Machines B and C produce an equal number of items.
2. Calculate the percentage of defective bolts produced by each machine:
- Machine A and B: 2% defect rate.
- Machine C: 4% defect rate.
3. Calculate the overall probability of selecting a defective bolt:
- Since all bolts are put into one stockpile, we need to consider the proportion of bolts produced by each machine.
- Let's assume that Machine B produces 1 unit. Then Machine A produces 2 units and Machine C also produces 1 unit.
- So the total production ratio is 1 (Machine B) : 2 (Machine A) : 1 (Machine C).
4. Calculate the total number of defective bolts:
- Since the defect rate for Machine A and B is 2%, and the proportion of their production is 2:1, we can calculate the number of defective bolts produced by A and B.
- For every 3 bolts produced by A and B, 2% are defective. So the number of defective bolts produced by A and B is (2/3) * 2% = 4/3%.
- The defect rate for Machine C is 4%, so the number of defective bolts produced by C is 4%.
- Summing up the defective bolts produced by A, B, and C, we get a total of (4/3)% + 4% = 16/3%.
5. Calculate the probability of choosing a defective bolt:
- The probability of choosing a defective bolt is equal to the total number of defective bolts divided by the total number of bolts in the stockpile.
- Since the defective bolts account for 16/3% of the total production, the probability of choosing a defective bolt is (16/3) / 100 = 16/300 = 0.0533.
6. Choose the closest option:
- The options provided are:
a) 0.075
b) 0.025
c) 0.15
d) 0.20
- The closest option to the calculated probability of 0.0533 is option b) 0.025.
Therefore, the correct answer is option b) 0.025, which represents the probability of choosing a defective bolt from the stockpile.
1. Determine the production ratios:
- Machine A produces twice as many items as Machine B.
- Machines B and C produce an equal number of items.
2. Calculate the percentage of defective bolts produced by each machine:
- Machine A and B: 2% defect rate.
- Machine C: 4% defect rate.
3. Calculate the overall probability of selecting a defective bolt:
- Since all bolts are put into one stockpile, we need to consider the proportion of bolts produced by each machine.
- Let's assume that Machine B produces 1 unit. Then Machine A produces 2 units and Machine C also produces 1 unit.
- So the total production ratio is 1 (Machine B) : 2 (Machine A) : 1 (Machine C).
4. Calculate the total number of defective bolts:
- Since the defect rate for Machine A and B is 2%, and the proportion of their production is 2:1, we can calculate the number of defective bolts produced by A and B.
- For every 3 bolts produced by A and B, 2% are defective. So the number of defective bolts produced by A and B is (2/3) * 2% = 4/3%.
- The defect rate for Machine C is 4%, so the number of defective bolts produced by C is 4%.
- Summing up the defective bolts produced by A, B, and C, we get a total of (4/3)% + 4% = 16/3%.
5. Calculate the probability of choosing a defective bolt:
- The probability of choosing a defective bolt is equal to the total number of defective bolts divided by the total number of bolts in the stockpile.
- Since the defective bolts account for 16/3% of the total production, the probability of choosing a defective bolt is (16/3) / 100 = 16/300 = 0.0533.
6. Choose the closest option:
- The options provided are:
a) 0.075
b) 0.025
c) 0.15
d) 0.20
- The closest option to the calculated probability of 0.0533 is option b) 0.025.
Therefore, the correct answer is option b) 0.025, which represents the probability of choosing a defective bolt from the stockpile.
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Community Answer
A bolt is manufactured by 3 machines A, B and C. Machine A turns out t...
Let A be the event in which an 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 = 2/100 (An item is defective, given that A has produced it)
P(D/B) = 2/100
P(D/C) = 4/100
P(C) = 1/4
By theorem of total productivity,
Required probability = Chosen a defective bolt from Machine A+ Chosen a defective bolt from Machine B+ Chosen a defective bolt from Machine C.
P(D) = P(A) × P(D/A) + P(B) × P(D/B) + P(C) × P(D/C)
=0.025
Hence, the correct option is (B).
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A bolt is manufactured by 3 machines A, B and C. Machine A turns out twice as many items as B and machines B and C produce an 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 put into 1 stockpile and 1 is chosen from this pile. What is the probability that it is defective?a)0.075b)0.025c)0.15d)0.20Correct answer is option 'B'. Can you explain this answer?
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A bolt is manufactured by 3 machines A, B and C. Machine A turns out twice as many items as B and machines B and C produce an 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 put into 1 stockpile and 1 is chosen from this pile. What is the probability that it is defective?a)0.075b)0.025c)0.15d)0.20Correct answer is option 'B'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about A bolt is manufactured by 3 machines A, B and C. Machine A turns out twice as many items as B and machines B and C produce an 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 put into 1 stockpile and 1 is chosen from this pile. What is the probability that it is defective?a)0.075b)0.025c)0.15d)0.20Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bolt is manufactured by 3 machines A, B and C. Machine A turns out twice as many items as B and machines B and C produce an 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 put into 1 stockpile and 1 is chosen from this pile. What is the probability that it is defective?a)0.075b)0.025c)0.15d)0.20Correct answer is option 'B'. Can you explain this answer?.
A bolt is manufactured by 3 machines A, B and C. Machine A turns out twice as many items as B and machines B and C produce an 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 put into 1 stockpile and 1 is chosen from this pile. What is the probability that it is defective?a)0.075b)0.025c)0.15d)0.20Correct answer is option 'B'. Can you explain this answer? for Computer Science Engineering (CSE) 2024 is part of Computer Science Engineering (CSE) preparation. The Question and answers have been prepared according to the Computer Science Engineering (CSE) exam syllabus. Information about A bolt is manufactured by 3 machines A, B and C. Machine A turns out twice as many items as B and machines B and C produce an 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 put into 1 stockpile and 1 is chosen from this pile. What is the probability that it is defective?a)0.075b)0.025c)0.15d)0.20Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A bolt is manufactured by 3 machines A, B and C. Machine A turns out twice as many items as B and machines B and C produce an 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 put into 1 stockpile and 1 is chosen from this pile. What is the probability that it is defective?a)0.075b)0.025c)0.15d)0.20Correct answer is option 'B'. Can you explain this answer?.
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ample number of questions to practice A bolt is manufactured by 3 machines A, B and C. Machine A turns out twice as many items as B and machines B and C produce an 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 put into 1 stockpile and 1 is chosen from this pile. What is the probability that it is defective?a)0.075b)0.025c)0.15d)0.20Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice Computer Science Engineering (CSE) tests.
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