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Determine whether the following events are mutually exclusive.

Select a student in your school: the student is a sophomore and enrolled in a business class.
A) Yes
B) No

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Final answer:

The events of being a sophomore and enrolled in a business class are not mutually exclusive because a student can be both simultaneously. Other examples illustrate that events which can occur simultaneously are not mutually exclusive. Additional context is needed for certain comparisons to determine exclusivity.

Step-by-step explanation:

To determine whether the events of a student being a sophomore and enrolled in a business class are mutually exclusive, we must establish if these two events can occur simultaneously. Mutually exclusive events cannot happen at the same time. Hence, if there existed a sophomore who is also enrolled in a business class, then these events would not be mutually exclusive. In most schools, it is certainly possible for a sophomore to take a business class. Therefore, the answer is B) No, and they are not mutually exclusive either.

Looking at another example, in a high school graduating class of 300, where 200 students are going to college, 40 are planning to work full-time, and 80 are taking a gap year, these events are not mutually exclusive since a student could both be going to college and working part-time, or even taking a gap year and working. The sum exceeds the total number of students, indicating overlap.

Regarding if milk and 30+ are mutually exclusive, it appears there was some missing context that prevented proper analysis, but generally, an item like 'milk' and an age range like '30+' are not related events and can't be classified without additional context.

For example, A and B are mutually exclusive if a blue card cannot also be a red or green card, making P(A AND B) = 0. If there's no commonality between events, they are mutually exclusive.

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