Exercises 69–72 use counting arguments from the preceding chapter. Intramurals The following five teams will be participating in Urban University ’s hockey intramural tournament: the Independent Wildcats, the Phi Chi Bulldogs, the Gate Crashers, the Slide Rule Nerds, and the City Slickers. Prizes will be awarded for the winner and runner-up. a. Find the cardinality n ( S ) of the sample space S of all possible outcomes of the tournament. (An outcome of the tournament consists of a winner and a runner-up.) b. Let E be the event that the City Slickers are runners-up, and let F be the event that the Independent Wildcats are neither the winners nor runners-up. Express the event E ∪ F in words, and find its cardinality.
Exercises 69–72 use counting arguments from the preceding chapter. Intramurals The following five teams will be participating in Urban University ’s hockey intramural tournament: the Independent Wildcats, the Phi Chi Bulldogs, the Gate Crashers, the Slide Rule Nerds, and the City Slickers. Prizes will be awarded for the winner and runner-up. a. Find the cardinality n ( S ) of the sample space S of all possible outcomes of the tournament. (An outcome of the tournament consists of a winner and a runner-up.) b. Let E be the event that the City Slickers are runners-up, and let F be the event that the Independent Wildcats are neither the winners nor runners-up. Express the event E ∪ F in words, and find its cardinality.
Exercises 69–72 use counting arguments from the preceding chapter.
Intramurals The following five teams will be participating in Urban University’s hockey intramural tournament: the Independent Wildcats, the Phi Chi Bulldogs, the Gate Crashers, the Slide Rule Nerds, and the City Slickers. Prizes will be awarded for the winner and runner-up.
a. Find the cardinality
n
(
S
)
of the sample space S of all possible outcomes of the tournament. (An outcome of the tournament consists of a winner and a runner-up.)
b. Let E be the event that the City Slickers are runners-up, and let F be the event that the Independent Wildcats are neither the winners nor runners-up. Express the event
E
∪
F
in words, and find its cardinality.
Definition Definition For any random event or experiment, the set that is formed with all the possible outcomes is called a sample space. When any random event takes place that has multiple outcomes, the possible outcomes are grouped together in a set. The sample space can be anything, from a set of vectors to real numbers.
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