If P(A) = 0.8, P(B) = 0.9, and P(A#nn#B)=.8, what is P(B|A)? What about P(A|B)?

1 Answer
Oct 28, 2015

#P(B|A) = 1#

#P(A|B) = 8/9 = 0.888dot#

Explanation:

If #P(A) = P(A|B)# then #AsubeB#
so given #B# it follows that #A# is certain.

One way to look at it is to suppose there were 1000 events
#P(A)=0.8# tells us that #800# of those events were of type #A#
#P(AnnB)=0.8# tells us that #800# of the #1000# are both #A# and #B#
So all the #A# events are "used up" in #(AnnB)#

Using the #1000# event example:
#P(B)=0.9# tells us #900# of the #1000# events are of type #B#

#800# of the #900# type #B# events are of type #A#,
so #P(A|B) = 800/900 = 8/9#