# Question: a certain illness has two symptoms associated with it ...

###### Question details

A certain illness has two symptoms associated with it - a fever
and fatigue. There is a 90% probability that *at least* one
of the two symptoms occurs for a randomly selected person with the
illness. There is an 80% probability that a randomly selected
person with the illness will come down with a fever and there is a
50% probability that a randomly selected person with the illness
will feel fatigued.

Please answer the following three questions:

1) Are the events of "fever" and "fatigue" mutually exclusive (or
disjoint)?

2) Are the events of "fever" and "fatigue" complementary?

3) Are the events of "fever" and "fatigue" independent?