2.3 Exercise 20

Data are $P \left(A\right) = 0 . 232$, $P \left(B\right) = 0 . 228$, $P \left(A B C\right) = 0 . 045$, $P \left(A C\right) = 0 . 062$,

$P \left(A B \cup A C \cup B C\right) = 0 . 197$ and $P \left(B C\right) = 2 P \left(A C\right)$.

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

Repeat, with the additional data $P \left(C\right) = 0 . 230$.