Final answer:
The probability of the complement of the union of two disjoint events A and B, where Pr(A) = 0.18 and Pr(B) = 0.31, is 0.51. This is calculated using the sum of their probabilities since they are disjoint, followed by applying the complement rule.
Step-by-step explanation:
The subject of the question is probability, a fundamental concept within the field of mathematics, more specifically the probability related to disjoint events or mutually exclusive events. When events A and B are disjoint, it means they cannot both occur at the same time. The probability of the union of A and B occurring, denoted as Pr(A ∪ B), is the sum of their individual probabilities since there's no overlap, Pr(A) + Pr(B). However, the question asks us to find the probability of the complement of this union, which is represented by Pr((A ∪ B)'). According to the complement rule in probability, the probability of the complement of an event is equal to 1 minus the probability of the event itself.
To calculate Pr((A ∪ B)'):
- Find Pr(A ∪ B), which is 0.18 + 0.31 = 0.49.
- Then apply the complement rule:
Pr((A ∪ B)') = 1 - Pr(A ∪ B) = 1 - 0.49 = 0.51.
Thus, the probability of the event Pr((A ∪ B)') is 0.51. This means that there is a 51% chance that neither event A nor event B will occur.
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