Final answer:
For a parallel structure of identical components, the probability of one component failing is 0.11, the probability of two components failing is 0.0121, and the probability that a parallel structure with 2 identical components will succeed is 0.78. To have a probability greater than 0.9999, you would need 8 components in the structure.
Step-by-step explanation:
To determine if it would be unusual to observe one or two components fail, we can calculate the probabilities of these events occurring using the given probability of each component failing.
(a) To find the probability of one component failing, we use the formula for the binomial distribution with n=1 and p=0.11. The probability of one component failing is 0.11
(b) To find the probability of two components failing, we use the same formula with n=2. The probability of two components failing is 0.0121
(c) To find the probability that a parallel structure with 2 identical components will succeed, we can use the complement rule. Since the probability of each component failing is 0.11, the probability of both components succeeding is 1 - 0.11 - 0.11 = 0.78.
(d) To find the number of components needed in the structure so that the probability of success is greater than 0.9999, we can use the complement rule again. The probability of the system failing is 1 - 0.9999 = 0.0001. We can solve for the number of components needed using the formula 0.11^n ≤ 0.0001. The smallest value of n that satisfies this inequality is 8.