2.3 Exercise 21

Data are: $P \left(A\right) = 0 . 4 , P \left(A B\right) = 0 . 3 , P \left(A B C\right) = 0 . 25 , P \left(C\right) = 0 . 65 ,$

$P \left(A^{c} C^{c}\right) = 0 . 3$. Determine available minterm probabilities and the following,

if computable:

With only six items of data (including $P \left(\Omega\right) = P \left(A \vee A^{c}\right) = 1$), not all minterms are available. Try the additional data $P \left(A^{c} B C^{c}\right) = 0 . 1$ and $P \left(A^{c} B^{c}\right) = 0 . 3$. Are these consistent and linearly independent? Are all minterm probabilities available?