SOLUTION: Given P(A)=0.23, P(B)=0.61, and P(A∩B)=0.18, what is P(A^c ∩B^c)

Question 1141770: Given P(A)=0.23, P(B)=0.61, and P(A∩B)=0.18, what is P(A^c ∩B^c)
Answer by ikleyn(52903) (Show Source): You can put this solution on YOUR website!
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Let us determine first what is the set  (A^c ∩ B^c).


It is the set of elements of the universal set that belong  NEITHER  "A"  NOR  "B".


In other words, it is the set  ((A U B)^c).


Therefore,  P(A^c ∩ B^c) = P((A U B)^c) = (it is the COMPLEMENT to P(A U B) ) = 1 - P(A U B).



Hence, to answer the problem's question, we need to find  P(A U B)  and then to take the complement to it.



Calculation of  P(A U B) is easy: it is


    P(A U B) = P(A) + P(B) - P(A ∩ B) = 0.23 + 0.61 - 0.18 = 0.66.


Therefore,  P(A^c ∩ B^c) = 1 - P(A U B) = 1 - 0.66 = 0.34.     ANSWER

Completed and solved.

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