# Math Help - Conditional probability proof

1. ## Conditional probability proof

The question is:

0 < P(A) < 1

Show that if P(B given A) > P(B) then P(B given A') < P(B)

2. Originally Posted by sharpe
The question is:

0 < P(A) < 1

Show that if P(B given A) > P(B) then P(B given A') < P(B)
$P(B|A)=\dfrac{P(B\cap A)}{P(A)}>P(B)$

$P(B|\overline{A})=\dfrac{P(B\cap \overline{A})}{P(\overline{A})}$

$P(A)+P(\overline{A})=1$

$P(B\cap A) + P(B\cap \overline{A})=P(B)$

Substitute..

3. Originally Posted by undefined
$P(B|A)=\dfrac{P(B\cap A)}{P(A)}>P(B)$

$P(B|\overline{A})=\dfrac{P(B\cap \overline{A})}{P(\overline{A})}$

$P(A)+P(\overline{A})=1$

$P(B\cap A) + P(B\cap \overline{A})=P(B)$

Substitute..

Great thanks - that is very helpful and looks all too simple now - thanks!