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! .
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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