Let A, B, and C be any three events defined on a sample space S. Show that (a) the outcomes in A ∪ ( B ∩ C ) are the same as the out-comes in ( A ∪ B ) ∩ ( A ∪ C ) . (b) the outcomes in A ∩ ( B ∪ C ) are the same as the out-comes in ( A ∩ B ) ∪ ( A ∩ C ) .
Let A, B, and C be any three events defined on a sample space S. Show that (a) the outcomes in A ∪ ( B ∩ C ) are the same as the out-comes in ( A ∪ B ) ∩ ( A ∪ C ) . (b) the outcomes in A ∩ ( B ∪ C ) are the same as the out-comes in ( A ∩ B ) ∪ ( A ∩ C ) .
Solution Summary: The author explains the verification of the outcomes in Acup (Bcap C) are the same as the results in
Let A, B, and C be any three events defined on a sample space S. Show that
(a) the outcomes in
A
∪
(
B
∩
C
)
are the same as the out-comes in
(
A
∪
B
)
∩
(
A
∪
C
)
.
(b) the outcomes in
A
∩
(
B
∪
C
)
are the same as the out-comes in
(
A
∩
B
)
∪
(
A
∩
C
)
.
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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