If A and B are two independent random variables, is P(A|B)<P(A)?

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Answer 1 · 2015-10-25T09:47:39

For independent variables #A# and #B# #P(A//B)=P(A)#

If variables #A# and #B# are independent, then

#P(AnnB)=P(A)*P(B)#.

According to definition of #P(A//B)#

#P(A//B)=(P(AnnB))/(P(B))#.

So:

#P(A//B)=(P(A)*P(B))/(P(B))#

So finally #P(A//B)=P(A)#