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A machine has three parts, A, B and C, whose chances of being defective are 0.02, 0.10 and 0.05 respectively. The machine stops working if any one of the parts becomes defective. What is the probability that the machine will not stop working?
- a)0.06
- b)0.16
- c)0.84
- d)0.94
Correct answer is option 'C'. Can you explain this answer?
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A machine has three parts, A, B and C, whose chances of being defectiv...
Probability that machine stops working
(∵ A, B & C are independent events)
∴ Probability that the machine will not stop working
Most Upvoted Answer
A machine has three parts, A, B and C, whose chances of being defectiv...
To find the probability that the machine will not stop working, we need to find the probability that all three parts of the machine are not defective.
Given probabilities:
- The chance of part A being defective is 0.02.
- The chance of part B being defective is 0.10.
- The chance of part C being defective is 0.05.
To find the probability that all three parts are not defective, we can calculate the complement of the probability that at least one part is defective.
Finding the probability of at least one defective part:
1. Find the probability of part A being defective: P(A) = 0.02.
2. Find the probability of part B being defective: P(B) = 0.10.
3. Find the probability of part C being defective: P(C) = 0.05.
4. Assume that the events of each part being defective are independent, meaning that the probability of one part being defective does not affect the probability of another part being defective.
5. Calculate the probability of at least one part being defective using the complement rule: P(at least one defective part) = 1 - P(no defective parts).
Calculating the probability of no defective parts:
1. Calculate the probability of part A not being defective: P(A') = 1 - P(A) = 1 - 0.02 = 0.98.
2. Calculate the probability of part B not being defective: P(B') = 1 - P(B) = 1 - 0.10 = 0.90.
3. Calculate the probability of part C not being defective: P(C') = 1 - P(C) = 1 - 0.05 = 0.95.
4. Since the events of each part being defective are independent, we can multiply the probabilities of each part not being defective to find the probability of all three parts not being defective: P(no defective parts) = P(A') * P(B') * P(C').
Calculating the probability of at least one defective part:
1. Calculate the probability of no defective parts: P(no defective parts) = P(A') * P(B') * P(C') = 0.98 * 0.90 * 0.95.
2. Calculate the probability of at least one defective part using the complement rule: P(at least one defective part) = 1 - P(no defective parts) = 1 - (0.98 * 0.90 * 0.95).
Therefore, the probability that the machine will not stop working is equal to the complement of the probability of at least one defective part: P(machine will not stop working) = 1 - P(at least one defective part).
Given that the correct answer is option 'C' (0.84), we can calculate the probability of at least one defective part and subtract it from 1 to find the probability that the machine will not stop working.
Given probabilities:
- The chance of part A being defective is 0.02.
- The chance of part B being defective is 0.10.
- The chance of part C being defective is 0.05.
To find the probability that all three parts are not defective, we can calculate the complement of the probability that at least one part is defective.
Finding the probability of at least one defective part:
1. Find the probability of part A being defective: P(A) = 0.02.
2. Find the probability of part B being defective: P(B) = 0.10.
3. Find the probability of part C being defective: P(C) = 0.05.
4. Assume that the events of each part being defective are independent, meaning that the probability of one part being defective does not affect the probability of another part being defective.
5. Calculate the probability of at least one part being defective using the complement rule: P(at least one defective part) = 1 - P(no defective parts).
Calculating the probability of no defective parts:
1. Calculate the probability of part A not being defective: P(A') = 1 - P(A) = 1 - 0.02 = 0.98.
2. Calculate the probability of part B not being defective: P(B') = 1 - P(B) = 1 - 0.10 = 0.90.
3. Calculate the probability of part C not being defective: P(C') = 1 - P(C) = 1 - 0.05 = 0.95.
4. Since the events of each part being defective are independent, we can multiply the probabilities of each part not being defective to find the probability of all three parts not being defective: P(no defective parts) = P(A') * P(B') * P(C').
Calculating the probability of at least one defective part:
1. Calculate the probability of no defective parts: P(no defective parts) = P(A') * P(B') * P(C') = 0.98 * 0.90 * 0.95.
2. Calculate the probability of at least one defective part using the complement rule: P(at least one defective part) = 1 - P(no defective parts) = 1 - (0.98 * 0.90 * 0.95).
Therefore, the probability that the machine will not stop working is equal to the complement of the probability of at least one defective part: P(machine will not stop working) = 1 - P(at least one defective part).
Given that the correct answer is option 'C' (0.84), we can calculate the probability of at least one defective part and subtract it from 1 to find the probability that the machine will not stop working.
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A machine has three parts, A, B and C, whose chances of being defective are 0.02, 0.10 and 0.05 respectively. The machine stops working if any one of the parts becomes defective. What is the probability that the machine will not stop working?a)0.06b)0.16c)0.84d)0.94Correct answer is option 'C'. Can you explain this answer?
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A machine has three parts, A, B and C, whose chances of being defective are 0.02, 0.10 and 0.05 respectively. The machine stops working if any one of the parts becomes defective. What is the probability that the machine will not stop working?a)0.06b)0.16c)0.84d)0.94Correct answer is option 'C'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about A machine has three parts, A, B and C, whose chances of being defective are 0.02, 0.10 and 0.05 respectively. The machine stops working if any one of the parts becomes defective. What is the probability that the machine will not stop working?a)0.06b)0.16c)0.84d)0.94Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A machine has three parts, A, B and C, whose chances of being defective are 0.02, 0.10 and 0.05 respectively. The machine stops working if any one of the parts becomes defective. What is the probability that the machine will not stop working?a)0.06b)0.16c)0.84d)0.94Correct answer is option 'C'. Can you explain this answer?.
A machine has three parts, A, B and C, whose chances of being defective are 0.02, 0.10 and 0.05 respectively. The machine stops working if any one of the parts becomes defective. What is the probability that the machine will not stop working?a)0.06b)0.16c)0.84d)0.94Correct answer is option 'C'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about A machine has three parts, A, B and C, whose chances of being defective are 0.02, 0.10 and 0.05 respectively. The machine stops working if any one of the parts becomes defective. What is the probability that the machine will not stop working?a)0.06b)0.16c)0.84d)0.94Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A machine has three parts, A, B and C, whose chances of being defective are 0.02, 0.10 and 0.05 respectively. The machine stops working if any one of the parts becomes defective. What is the probability that the machine will not stop working?a)0.06b)0.16c)0.84d)0.94Correct answer is option 'C'. Can you explain this answer?.
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