Simplify and select the answer with the appropriate restrictions for the variables.
1 answer:
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Answer:
Step-by-step explanation:
From the given information:
a.
Compute :
b.
Compute P(A ∩ B)
P(A ∩ B) = P(A) +P(B) - P(A∪B)
P(A ∩ B) = 0.32 + 0.46 - 0.57
P(A ∩ B) = 0.21
Thus, since P(A ∩ B) ≠ 0, we can say that they are not mutually exclusive.
c.
P(A ∩ C) = P(A) +P(C) - P(A∪C)
P(A ∩ C) = 0.32 + 0.23 -0.55
P(A ∩ C) = 0
Thus, since P(A ∩ C) = 0, we can say that they are both mutually exclusive.
d. To determine P[(A ∪ B ∪ C)′]
i.e. none of the events occurring
Then :
P(B ∩ C) = 0.46 +0.23 -0.49
P(B ∩ C) = 0.20
Therefore:
P(A ∪ B ∪ C) = P(A) + P(B) + P(C) - P(A ∩ B ) - P(A ∩ C) - P(B ∩ C) + P(A ∩ B ∩ C)
P(A ∪ B ∪ C) = 0.32 + 0.46 + 0.23 - 0.21 - 0 - 0.20 + 0
P(A ∪ B ∪ C) = 0.60