Let S = { s 1 , s 2 , s 3 , s 4 , s 5 , s 6 } be the sample space associated with an experiment having the probability distribution shown in the accompanying table. If A = { s 1 , s 2 } and B = { s 1 , s 5 , s 6 } , find: a. P ( A ) , P ( B ) b. P ( A C ) , P ( B C ) c. P ( A ∩ B ) d. P ( A ∪ B ) e. P ( A C ∩ B C ) f. P ( A C ∪ B C ) Outcome Probability s 1 1 3 s 2 1 8 s 3 1 6 s 4 1 6 s 5 1 12 s 6 1 8
Let S = { s 1 , s 2 , s 3 , s 4 , s 5 , s 6 } be the sample space associated with an experiment having the probability distribution shown in the accompanying table. If A = { s 1 , s 2 } and B = { s 1 , s 5 , s 6 } , find: a. P ( A ) , P ( B ) b. P ( A C ) , P ( B C ) c. P ( A ∩ B ) d. P ( A ∪ B ) e. P ( A C ∩ B C ) f. P ( A C ∪ B C ) Outcome Probability s 1 1 3 s 2 1 8 s 3 1 6 s 4 1 6 s 5 1 12 s 6 1 8
Solution Summary: The author explains how the probability of the event can be calculated by the formula shown below.
Let
S
=
{
s
1
,
s
2
,
s
3
,
s
4
,
s
5
,
s
6
}
be the sample space associated with an experiment having the probability distribution shown in the accompanying table. If
A
=
{
s
1
,
s
2
}
and
B
=
{
s
1
,
s
5
,
s
6
}
, find:
a.
P
(
A
)
,
P
(
B
)
b.
P
(
A
C
)
,
P
(
B
C
)
c.
P
(
A
∩
B
)
d.
P
(
A
∪
B
)
e.
P
(
A
C
∩
B
C
)
f.
P
(
A
C
∪
B
C
)
Outcome
Probability
s
1
1
3
s
2
1
8
s
3
1
6
s
4
1
6
s
5
1
12
s
6
1
8
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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