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.
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