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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 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 airline‘s flights suffer a minor equipment fa...
Given:
- Probability of minor equipment failure in an aircraft = 1%
- Total number of flights = 100

To find:
- Probability of exactly two minor equipment failures in 100 flights

Solution:
- This problem can be solved using the binomial distribution formula:
P(x) = nCx * p^x * (1-p)^(n-x)
where n = total number of trials, p = probability of success, x = number of successes

- Here, x = 2 (we want exactly two minor equipment failures)
- n = 100 (total number of flights)
- p = 0.01 (probability of minor equipment failure)

- Plugging in these values, we get:
P(2) = 100C2 * 0.01^2 * 0.99^98
where 100C2 = 100! / (2! * 98!) = 4950

- Simplifying the expression, we get:
P(2) = 4950 * 0.0001 * 0.1326
= 0.0657

- Therefore, the probability of exactly two minor equipment failures in 100 flights is 0.0657 or 6.57%.

- However, the answer choices are given in decimal format, so we need to convert the answer to decimal form:
0.0657 = 6.57/100 = 0.0657

- The closest answer choice to 0.0657 is option B, which is 0.184. Therefore, the correct answer is option B.
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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 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?
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