If U 1 and U 2 are two mutually exclusive events whose union is the equally likely sample space S and if E is an arbitrary event in S such that P E ≠ 0 , show that P U 1 E = n U 1 ∩ E n U 1 ∩ E + n U 2 ∩ E
If U 1 and U 2 are two mutually exclusive events whose union is the equally likely sample space S and if E is an arbitrary event in S such that P E ≠ 0 , show that P U 1 E = n U 1 ∩ E n U 1 ∩ E + n U 2 ∩ E
Solution Summary: The author explains how to prove the formula P(U_1|E)=n
If
U
1
and
U
2
are two mutually exclusive events whose union is the equally likely sample space
S
and if
E
is an arbitrary event in
S
such that
P
E
≠
0
, show that
P
U
1
E
=
n
U
1
∩
E
n
U
1
∩
E
+
n
U
2
∩
E
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.
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
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