2.3 Exercise 6

Suppose $P \left(A \cup B^{c} C\right) = 0 . 65 , P \left(A C\right) = 0 . 2 , P \left(A^{c} B\right) = 0 . 25$

$P \left(A^{c} C^{c}\right) = 0 . 25 , P \left(B C^{c}\right) = 0 . 30$. Determine $P \left(\left(A C^{c} \cup A^{c} C\right)B^{c}\right)$.

Then determine $P \left(\left(A B^{c} \cup A^{c}\right)C^{c}\right)$ and $P \left(A^{c} \left(B \cup C^{c}\right)\right)$, if possible.