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If 1 percent of an airline's flights suffer a minor equipment failure in an aircraft, what is the probability that there will be exactly that  there will be exactly two such failures in the next 100 such flights?
  • a)
    0.50
  • b)
    0.184
  • c)
    0.265
  • d)
    0.256
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
If 1 percent of an airlines flights suffer a minor equipment failure i...
Probability of Minor Equipment Failure
Given that 1% of an airline's flights suffer a minor equipment failure, the probability of such a failure occurring in any one flight is 0.01.

Probability of Two Failures in 100 Flights
To calculate the probability of exactly two failures occurring in the next 100 flights, we can use the binomial probability formula. This formula is given by:
P(X = k) = C(n, k) * p^k * (1 - p)^(n-k)
Where:
- P(X = k) is the probability of getting exactly k successes in n trials
- C(n, k) is the number of combinations of n items taken k at a time
- p is the probability of success on any one trial
- n is the number of trials
- k is the number of successes
In this case, n = 100, p = 0.01, and we are interested in k = 2.

Calculating the Probability
Plugging these values into the formula, we get:
P(X = 2) = C(100, 2) * 0.01^2 * (1 - 0.01)^(100-2)
P(X = 2) = 4950 * 0.0001 * 0.99^98
P(X = 2) ≈ 0.184
Therefore, the probability that there will be exactly two minor equipment failures in the next 100 flights is approximately 0.184, which corresponds to option B.
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If 1 percent of an airlines flights suffer a minor equipment failure in an aircraft, what is the probability that there will be exactly that there will be exactly two such failures in the next 100 such flights?a)0.50b)0.184c)0.265d)0.256Correct answer is option 'B'. Can you explain this answer?
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