University of California, San Diego
ECE109:
Problem Set #1
1.
An ice cream store manufactures five basic flavors (vanilla, chocolate, mint, strawberry, and
fudge) of ice cream, and then creates its specialty flavors by mixing two or more basic flavors in
equal proportions.
(
a)
How many specialty flavors can be obtained by mixing three basic flavors? How many of
these contain chocolate? How many of these contain either chocolate or fudge or both?
How many of these contain either chocolate or fudge but not both?
(
b)
How many distinct flavors (including basic and specialty flavors) of ice cream can the store
offer?
2.
Express each of the following events in terms of the events
, and
, and the operations of
complementation, union, and intersection:
(a) at least one of the events
occurs;
(b) at most one of the events
occurs;
(c) none of the events
occurs;
(d) all three events
occur;
(e) exactly one of the events
occurs;
(f) events
and
occur, but not
;
(g) either event
occurs, or if not then
also does not occur.
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 Winter '09
 staff
 Probability theory, San Diego, ECE109

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