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Problem 5. Let A, B and C be pairwise disjoint subsets of the sample space. For each one of the following statements, determine whether it is true or false. Note: \"False\" means \"It is not always true.\" (a) $P(A^c) + P(B) \le 1$ (b) $P(A) + P(B) \le 1$ (c) $P(A \cup B \cup C) \ge P(A \cup C)$ Problem 6. A certain system can experience three different types of defects. Let $A_i$ (i= 1,2,3) denote the event that the system has a defect of type i. Suppose that $P(A_1) = 0.12$, $P(A_2) = 0.07$, $P(A_3) = 0.05$ $P(A_1 \cup A_2) = 0.13$, $P(A_1 \cup A_3) = 0.14$, $P(A_2 \cup A_3) = 0.10$, $P(A_1 \cap A_2 \cap A_3) = 0.01$. a. What is the probability that the system does not have a type 1 defect? b. What is the probability that the system has both type 1 and type 2 defects? c. What is the probability that the system has both type 1 and type 2 defects but not a type 3 defect? d. What is the probability that the system has at most two of these defects?

          Problem 5. Let A, B and C be pairwise disjoint subsets of the sample space.
For each one of the following statements, determine whether it is true or false.
Note: \"False\" means \"It is not always true.\"
(a) $P(A^c) + P(B) \le 1$
(b) $P(A) + P(B) \le 1$
(c) $P(A \cup B \cup C) \ge P(A \cup C)$
Problem 6. A certain system can experience three different types of defects.
Let $A_i$ (i= 1,2,3) denote the event that the system has a defect of type i.
Suppose that
$P(A_1) = 0.12$, $P(A_2) = 0.07$, $P(A_3) = 0.05$
$P(A_1 \cup A_2) = 0.13$, $P(A_1 \cup A_3) = 0.14$, $P(A_2 \cup A_3) = 0.10$,
$P(A_1 \cap A_2 \cap A_3) = 0.01$.
a. What is the probability that the system does not have a type 1 defect?
b. What is the probability that the system has both type 1 and type 2
defects?
c. What is the probability that the system has both type 1 and type 2
defects but not a type 3 defect?
d. What is the probability that the system has at most two of these defects?

Problem 5. Let A, B and C be pairwise disjoint subsets of the sample space.
For each one of the following statements, determine whether it is true or false.
Note: F̈alsem̈eans Ït is not always true.(̈a) P(A^c) + P(B) ≤ 1
(b) P(A) + P(B) ≤ 1
(c) P(A ∪ B ∪ C) ≥ P(A ∪ C)
Problem 6. A certain system can experience three different types of defects.
Let Ai (i= 1,2,3) denote the event that the system has a defect of type i.
Suppose that
P(A1) = 0.12, P(A2) = 0.07, P(A3) = 0.05
P(A1 ∪ A2) = 0.13, P(A1 ∪ A3) = 0.14, P(A2 ∪ A3) = 0.10,
P(A1 ∩ A2 ∩ A3) = 0.01.
a. What is the probability that the system does not have a type 1 defect?
b. What is the probability that the system has both type 1 and type 2
defects?
c. What is the probability that the system has both type 1 and type 2
defects but not a type 3 defect?
d. What is the probability that the system has at most two of these defects?

Added by Kerri M.

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