Let A and B be two events defined on a sample space S such that P ( A ∩ B C ) = 0.1 , P ( A C ∩ B ) = 0.3 , and P ( ( A ∪ B ) C ) = 0.2 . Find the probability that at least one of the two events occurs given that at most one occurs.
Let A and B be two events defined on a sample space S such that P ( A ∩ B C ) = 0.1 , P ( A C ∩ B ) = 0.3 , and P ( ( A ∪ B ) C ) = 0.2 . Find the probability that at least one of the two events occurs given that at most one occurs.
Solution Summary: The author explains that the probability that at least one of the two events occurs is 2/3.
Let A and B be two events defined on a sample space S such that
P
(
A
∩
B
C
)
=
0.1
,
P
(
A
C
∩
B
)
=
0.3
, and
P
(
(
A
∪
B
)
C
)
=
0.2
. Find the probability that at least one of the two events occurs given that at most one occurs.
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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