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Mathematics
Mathematics
Problem
Let
E
1
E_1
E
1
and
E
2
E_2
E
2
be events forming a partition of the sample space with
P
(
E
1
)
=
p
P(E_1)=p
P
(
E
1
)
=
p
and
P
(
E
2
)
=
1
−
p
P(E_2)=1-p
P
(
E
2
)
=
1
−
p
. For another event
A
A
A
, it is known that
P
(
A
∣
E
1
)
=
0.7
P(A\mid E_1)=0.7
P
(
A
∣
E
1
)
=
0.7
,
P
(
A
∣
E
2
)
=
0.4
P(A\mid E_2)=0.4
P
(
A
∣
E
2
)
=
0.4
and
P
(
A
)
=
0.55
P(A)=0.55
P
(
A
)
=
0.55
. Determine the value of
p
p
p
.
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