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The probability that GATE CS/IT question has an error is 1/20 and 65 questions are made in such an exam. If the probability that at least 2 question has an error is [1−[a(19/20)64]] then what is the value of a (answer up to 2 decimal place)?
Correct answer is '4.2'. Can you explain this answer?
Verified Answer
The probability that GATE CS/IT question has an error is 1/20 and 65 q...
Using Binomial Distribution
Probability that x questions have an error
Probability that x questions have an error
Most Upvoted Answer
The probability that GATE CS/IT question has an error is 1/20 and 65 q...
Understanding the Problem
The problem is about calculating the probability of errors in questions on a GATE CS/IT exam. Given that the probability of a question having an error is 1/20 (or 0.05), we can analyze the situation using the complementary probability.
Calculating the Complementary Probability
- The probability that a question does not have an error is 1 - (1/20) = 19/20.
- For 65 questions, the probability that none of them have errors is (19/20)^65.
- The probability that at least 2 questions have errors can be calculated as:
P(at least 2 errors) = 1 - P(0 errors) - P(1 error)
Calculating the Individual Probabilities
1. No Errors:
- P(0 errors) = (19/20)^65
2. Exactly One Error:
- For exactly one error, we choose 1 question to have an error and the rest not:
- P(1 error) = C(65, 1) * (1/20)^1 * (19/20)^64
- C(65, 1) = 65 (the number of ways to choose 1 question from 65)
Therefore, P(1 error) = 65 * (1/20) * (19/20)^64.
Final Calculation
Combining these probabilities:
P(at least 2 errors) = 1 - [(19/20)^65 + 65 * (1/20) * (19/20)^64].
This can be factored as:
P(at least 2 errors) = 1 - [a * (19/20)^64], where a = (19/20) + 65 * (1/20).
Calculating a:
- a = (19/20) + 65 * (1/20) = (19 + 65) / 20 = 84 / 20 = 4.2.
Conclusion
Thus, the value of "a" is 4.2, which matches the given correct answer.
The problem is about calculating the probability of errors in questions on a GATE CS/IT exam. Given that the probability of a question having an error is 1/20 (or 0.05), we can analyze the situation using the complementary probability.
Calculating the Complementary Probability
- The probability that a question does not have an error is 1 - (1/20) = 19/20.
- For 65 questions, the probability that none of them have errors is (19/20)^65.
- The probability that at least 2 questions have errors can be calculated as:
P(at least 2 errors) = 1 - P(0 errors) - P(1 error)
Calculating the Individual Probabilities
1. No Errors:
- P(0 errors) = (19/20)^65
2. Exactly One Error:
- For exactly one error, we choose 1 question to have an error and the rest not:
- P(1 error) = C(65, 1) * (1/20)^1 * (19/20)^64
- C(65, 1) = 65 (the number of ways to choose 1 question from 65)
Therefore, P(1 error) = 65 * (1/20) * (19/20)^64.
Final Calculation
Combining these probabilities:
P(at least 2 errors) = 1 - [(19/20)^65 + 65 * (1/20) * (19/20)^64].
This can be factored as:
P(at least 2 errors) = 1 - [a * (19/20)^64], where a = (19/20) + 65 * (1/20).
Calculating a:
- a = (19/20) + 65 * (1/20) = (19 + 65) / 20 = 84 / 20 = 4.2.
Conclusion
Thus, the value of "a" is 4.2, which matches the given correct answer.
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The probability that GATE CS/IT question has an error is 1/20 and 65 questions are made in such an exam. If the probability that at least 2 question has an error is[1−[a(19/20)64]] then what is the value ofa(answer up to 2 decimal place)?Correct answer is '4.2'. Can you explain this answer? for Computer Science Engineering (CSE) 2025 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 The probability that GATE CS/IT question has an error is 1/20 and 65 questions are made in such an exam. If the probability that at least 2 question has an error is[1−[a(19/20)64]] then what is the value ofa(answer up to 2 decimal place)?Correct answer is '4.2'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The probability that GATE CS/IT question has an error is 1/20 and 65 questions are made in such an exam. If the probability that at least 2 question has an error is[1−[a(19/20)64]] then what is the value ofa(answer up to 2 decimal place)?Correct answer is '4.2'. Can you explain this answer?.
The probability that GATE CS/IT question has an error is 1/20 and 65 questions are made in such an exam. If the probability that at least 2 question has an error is[1−[a(19/20)64]] then what is the value ofa(answer up to 2 decimal place)?Correct answer is '4.2'. Can you explain this answer? for Computer Science Engineering (CSE) 2025 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 The probability that GATE CS/IT question has an error is 1/20 and 65 questions are made in such an exam. If the probability that at least 2 question has an error is[1−[a(19/20)64]] then what is the value ofa(answer up to 2 decimal place)?Correct answer is '4.2'. Can you explain this answer? covers all topics & solutions for Computer Science Engineering (CSE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The probability that GATE CS/IT question has an error is 1/20 and 65 questions are made in such an exam. If the probability that at least 2 question has an error is[1−[a(19/20)64]] then what is the value ofa(answer up to 2 decimal place)?Correct answer is '4.2'. Can you explain this answer?.
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