Events C and D are mutually exclusive because a number cannot be both odd and even, whereas events C and E are not mutually exclusive as they share a common result, the number 3, which is both less than five and odd.
The question concerns whether certain sets of numbers that represent faces of a die are mutually exclusive events.
Event C includes all odd numbers greater than two, so C = {3, 5}.
Event D encompasses all even numbers less than five, hence D = {2, 4}.
Because a number cannot be both odd and even simultaneously, P(C AND D) = 0, confirming that events C and D are mutually exclusive.
In contrast, when looking at event E, which includes all numbers less than five (E = {1, 2, 3, 4}), we see that it is not mutually exclusive with event C.
The reason is that there are numbers that belong to both C and E, specifically the number 3.
Since both events can occur at the same time (a die showing a face with three, which is less than five and odd), they are not mutually exclusive.
The probable question may be:
Explain why the above graph is guaranteed to contain at least one Euler path.
A. The graph is guaranteed to contain at least one Euler path since the graph contains no odd vertices.
B. The graph is guaranteed to contain at least one Euler path since all graphs must contain an Euler path.
C. The graph is guaranteed to contain at least one Euler path since the graph contains exactly two even vertices.
D. The graph is guaranteed to contain at least one Euler path since the graph contains more than two odd
vertices.
E. The graph is guaranteed to contain at least one Euler path since the graph contains exactly two odd vertices.
Starting at vertex C, find an Euler path for the graph whose fourth and seventh vertices are E and fifth vertex is D. Report the solution as a sequence of vertices (e.g., ABCDE or AECDCACBEA).