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If 1 per cent of an airline's flights suffer a minor equipment failure in n aircraft, what is the probability that there will be exactly two such failures in the next 100 such flights?
Most Upvoted Answer
If 1 per cent of an airline's flights suffer a minor equipment failure...
Probability of Minor Equipment Failure
- The probability of a minor equipment failure in a single flight is 1% or 0.01.
- Let's denote this probability as p = 0.01.
Probability of Two Failures in 100 Flights
- In the next 100 flights, we want to find the probability of exactly two minor equipment failures.
- This situation can be modeled using the binomial distribution formula:
P(X = k) = (n choose k) * p^k * (1-p)^(n-k)
where n is the number of trials, k is the number of successes, p is the probability of success, and (n choose k) is the combination formula.
Calculation
- In this case, n = 100, p = 0.01, and we want k = 2 minor equipment failures.
- Plugging these values into the formula:
P(X = 2) = (100 choose 2) * 0.01^2 * 0.99^98
- Calculating (100 choose 2) = 4950, 0.01^2 = 0.0001, and 0.99^98 ≈ 0.366.
- Therefore, P(X = 2) ≈ 4950 * 0.0001 * 0.366 ≈ 0.1814.
Conclusion
- The probability that there will be exactly two minor equipment failures in the next 100 flights is approximately 0.1814 or 18.14%.
- The probability of a minor equipment failure in a single flight is 1% or 0.01.
- Let's denote this probability as p = 0.01.
Probability of Two Failures in 100 Flights
- In the next 100 flights, we want to find the probability of exactly two minor equipment failures.
- This situation can be modeled using the binomial distribution formula:
P(X = k) = (n choose k) * p^k * (1-p)^(n-k)
where n is the number of trials, k is the number of successes, p is the probability of success, and (n choose k) is the combination formula.
Calculation
- In this case, n = 100, p = 0.01, and we want k = 2 minor equipment failures.
- Plugging these values into the formula:
P(X = 2) = (100 choose 2) * 0.01^2 * 0.99^98
- Calculating (100 choose 2) = 4950, 0.01^2 = 0.0001, and 0.99^98 ≈ 0.366.
- Therefore, P(X = 2) ≈ 4950 * 0.0001 * 0.366 ≈ 0.1814.
Conclusion
- The probability that there will be exactly two minor equipment failures in the next 100 flights is approximately 0.1814 or 18.14%.
Community Answer
If 1 per cent of an airline's flights suffer a minor equipment failure...
100c2 * (1/100)^2*(99/100)^98 may be ur answer
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If 1 per cent of an airline's flights suffer a minor equipment failure in n aircraft, what is the probability that there will be exactly two such failures in the next 100 such flights?
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If 1 per cent of an airline's flights suffer a minor equipment failure in n aircraft, what is the probability that there will be exactly two such failures in the next 100 such flights? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If 1 per cent of an airline's flights suffer a minor equipment failure in n aircraft, what is the probability that there will be exactly two such failures in the next 100 such flights? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 1 per cent of an airline's flights suffer a minor equipment failure in n aircraft, what is the probability that there will be exactly two such failures in the next 100 such flights?.
If 1 per cent of an airline's flights suffer a minor equipment failure in n aircraft, what is the probability that there will be exactly two such failures in the next 100 such flights? for CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about If 1 per cent of an airline's flights suffer a minor equipment failure in n aircraft, what is the probability that there will be exactly two such failures in the next 100 such flights? covers all topics & solutions for CA Foundation 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If 1 per cent of an airline's flights suffer a minor equipment failure in n aircraft, what is the probability that there will be exactly two such failures in the next 100 such flights?.
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