Suppose that A, B, and C are three events that cannot all occur simultaneously.
Does this condition necessarily imply that A, B, and C are mutually exclusive?
Mutually Exclusive Events
Let there be any two events. If the possibility of happening of these two events together at all points of time is zero, these events are said to be mutually exclusive or disjoint events. For example occurrence of number 3 and number 6 on rolling a fair six-sided dice is an example of the mutually exclusive event.
Answer and Explanation:
It is given that the three events A, B, C cannot occur together at all. But there is a possibility that the events A or B, or events B or C, or events A or C can occur together. On such happening, the events A, B and C will not be mutually exclusive then.
Hence if events A, B, and C cannot all occur simultaneously, does not necessarily mean that A, B, and C are mutually exclusive.
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from High School Algebra II: Help and ReviewChapter 25 / Lesson 8