2.3 Exercise 18

Suppose $P \left(A\left(B \cup C\right)\right) = 0 . 3 , P \left(A^{c}\right) = 0 . 6 , \text{and} P \left(A^{c} B^{c} C^{c}\right) = 0 . 1$.

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

Repeat the problem with the additional data $P \left(A^{c} B C\right) = 0 . 2$ and $P \left(A^{c} B\right) = 0 . 3$.