Let p=0.2 and q=0.5. Which two events from below are mutually exclusive? Select two events.

Question

BlackTom AI · Accepted Answer

To determine mutual exclusivity, we check whether two events cannot occur at the same time.
Option-by-option analysis:
- X >= 0: This event is true for all nonnegative values of X. It is a universal truth in common contexts, so it cannot be mutually exclusive with any other event that could also occur (since if X >= 0 is true, the other event could still be true as well). For example, X >= 0 is true whenever X >= 20 is true, so they are not exclusive; they can both occur.
- Y >= 0: Similarly, this kind of lower-bound event for Y is typically always true (assuming Y takes nonnegative values). If Y >= 0 is always true, it cannot be mutually exclusive with any other event that could occur, because both could be true simultaneously. Even if we compare it to Y >= 10, Y >= 10 implies Y >= 0, so they are not mutually exclusive either.
- X >= 20: This is a stronger condition than X >= 10 or X >= 0. Any outcome with X >= 20 also satisfies X >= 10 and X >= 0, so these pairs are not mutually exclusive; they are nested and can occur together as X grows.
- X >= 10: This is also nested with X >= 0 (any X >= 10 satisfies X >= 0) and with X >= 20 (X >= 20 implies X >= 10). Therefore, X >= 10 cannot be mutually exclusive with X >= 0 or X >= 20.
- Y >= 10: The same reasoning as for Y >= 0 applies. If Y can reach values >= 10, it already satisfies Y >= 0, so Y >= 10 and Y >= 0 are not mutually exclusive; they can both occur.
In summary, for the common interpretations of these inequalities, none of the listed single events are mutually exclusive with another, because many of them are nested (one implies the other) or are always-true bounds, which allows simultaneous occurrence.
Given this, there is no pair among the provided options that are mutually exclusive. The attempt to select two events that are mutually exclusive would be inconsistent with these standard relationships between the inequalities.

Let p=0.2 and q=0.5. Which two events from below are mutually exclusive? Select two events. 多项选择题

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