Question 1203558
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If A and B are events, show that:
(a) P(A n B') = P(A) - P(A n B)
(b) P(A u B) = i - P(A' n B')
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<pre>
(a)  P(A n B')  in the left side  is the probability of events that belong A and B' ; 

                in other words, it is the probability of events that belong A but do not belong B.


     P(A) - P(A n B)  in the right side  is the probability of events that belong to A but do not belong to B.

                  +--------------------------------------------------+
                  |    So, in both sides we have equal quantities.   |
                  |          Thus statement (a) is proved.           |
                  +--------------------------------------------------+



(b)  P(A U B) in the left side is the probability of events that belong A or B.

     P(A' n B') in the right side is the probability of events that do belong NEITHER A NOR B.

     At this point, it is clear that probabilities  P(A U B)  and  P(A' n B')  are supplementary.

     It is exactly what the statement (b) means.


                  +--------------------------------------------------+
                  |         Thus statement (b) is proved.            |
                  +--------------------------------------------------+
</pre>

Solved.