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Grinstead-Snell-Probability
· Problem 4.1.51
Conditional Probability
Mathematics · conditional-probability-inequality
Problem
Prove that if
P
(
A
∣
C
)
≥
P
(
B
∣
C
)
and
P
(
A
∣
C
~
)
≥
P
(
B
∣
C
~
)
,
P(A|C) \geq P(B|C) \quad \text{and} \quad P(A|\tilde{C}) \geq P(B|\tilde{C}),
P
(
A
∣
C
)
≥
P
(
B
∣
C
)
and
P
(
A
∣
C
~
)
≥
P
(
B
∣
C
~
)
,
then
P
(
A
)
≥
P
(
B
)
P(A) \geq P(B)
P
(
A
)
≥
P
(
B
)
.
Related theory
Conditional Probability
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