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Consider a company that assembles computers. The probability of a faulty assembly of any computer is p. The company, therefore, subjects each computer to a testing process. This testing process gives the correct result for any computer with a probability of q.
What is the probability of a computer being declared faulty?
What is the probability of a computer being declared faulty?
- a)pq + (1-p)(1-q)
- b)(1-q)p
- c)(1-p)q
- d)pq
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Consider a company that assembles computers. The probability of a faul...
Probability of a computer being declared faulty
To calculate the probability of a computer being declared faulty, we need to consider the probabilities of two independent events: the assembly of a faulty computer and the testing process giving the correct result.
Given Information:
- Probability of a faulty assembly of any computer: p
- Probability of the testing process giving the correct result: q
Approach:
To find the probability of a computer being declared faulty, we need to consider two scenarios:
1. The computer is faulty and the testing process gives the correct result.
2. The computer is not faulty and the testing process gives an incorrect result.
Scenario 1: The computer is faulty and the testing process gives the correct result.
The probability of a computer being faulty is p, and the probability of the testing process giving the correct result is q. Since these two events are independent, we can multiply their probabilities to find the probability of both events occurring simultaneously. Therefore, the probability of a computer being faulty and the testing process giving the correct result is pq.
Scenario 2: The computer is not faulty and the testing process gives an incorrect result.
The probability of a computer not being faulty is (1 - p), and the probability of the testing process giving an incorrect result is (1 - q). Again, since these two events are independent, we can multiply their probabilities to find the probability of both events occurring simultaneously. Therefore, the probability of a computer not being faulty and the testing process giving an incorrect result is (1 - p)(1 - q).
Conclusion:
The probability of a computer being declared faulty is the sum of the probabilities from both scenarios:
- Scenario 1: pq
- Scenario 2: (1 - p)(1 - q)
Therefore, the total probability of a computer being declared faulty is pq + (1 - p)(1 - q).
To calculate the probability of a computer being declared faulty, we need to consider the probabilities of two independent events: the assembly of a faulty computer and the testing process giving the correct result.
Given Information:
- Probability of a faulty assembly of any computer: p
- Probability of the testing process giving the correct result: q
Approach:
To find the probability of a computer being declared faulty, we need to consider two scenarios:
1. The computer is faulty and the testing process gives the correct result.
2. The computer is not faulty and the testing process gives an incorrect result.
Scenario 1: The computer is faulty and the testing process gives the correct result.
The probability of a computer being faulty is p, and the probability of the testing process giving the correct result is q. Since these two events are independent, we can multiply their probabilities to find the probability of both events occurring simultaneously. Therefore, the probability of a computer being faulty and the testing process giving the correct result is pq.
Scenario 2: The computer is not faulty and the testing process gives an incorrect result.
The probability of a computer not being faulty is (1 - p), and the probability of the testing process giving an incorrect result is (1 - q). Again, since these two events are independent, we can multiply their probabilities to find the probability of both events occurring simultaneously. Therefore, the probability of a computer not being faulty and the testing process giving an incorrect result is (1 - p)(1 - q).
Conclusion:
The probability of a computer being declared faulty is the sum of the probabilities from both scenarios:
- Scenario 1: pq
- Scenario 2: (1 - p)(1 - q)
Therefore, the total probability of a computer being declared faulty is pq + (1 - p)(1 - q).
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Community Answer
Consider a company that assembles computers. The probability of a faul...
From the diagram,
Pdeclared faulty = pq + (1 − p) (1 − q )
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