Question
If two events are collectively exhaustive, what is the probability that one or the other 0.25 0.50 1.00 This cannot be determined from the information given.
Ask by Kirk Huff. in the United States
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The probability that one or the other event occurs is \(1.00\).
Solution
1. Two events are collectively exhaustive if their union covers the entire sample space. This means that when one event does not occur, the other must occur.
2. Therefore, the probability that one or the other event occurs is the probability of the entire sample space, which is \(1\).
Final answer: \(1.00\).
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Simplify this solution Mind Expander
When two events are collectively exhaustive, it means that together they encompass all possible outcomes of a given situation. In simpler terms, there are no outcomes left out; one of the events must happen. Therefore, the probability that at least one of the events occurs is always 1.00—it's a certainty! In practical scenarios, you might encounter collective exhaustiveness in game shows or decision-making processes. For instance, if a contestant must choose between two options, like "stay" or "go," these choices cover all possible actions. Thus, no matter what happens, one of those decisions is guaranteed to be the winner!
