There are 4 different event, $A$, $B$, $C$, and $D$, and the probability are 0.3, 0.4, 0.6, and 0.7, respectively, but we don't know the joint probability of any of them.
Additionally, we already know that there must be exact 2 events occur among those 4.
Is the information given above enough to calculate $P(B|¬A)$?
Thanks.
$ \textbf {Example I}$: draw an integer uniformly from $\{1, \cdots, 10\}$. Define our events as
$$A_1=\{1,2,3\}\quad B_1=\{7,8,9,10\} \quad C_1=\{1,2,3,4,5,6\}\quad D_1=\{4,5,6,7,8,9,10\}$$
We see that, as desired, each draw belongs to exactly two of your events, and we see that $P(B_1\,|\,A_1^c)=\frac 47$
$ \textbf {Example II}$: Same process. Now define $$A_2=\{1,2,3\}\quad B_2=\{1,2,3,4\} \quad C_2=\{5,6,7,8,9,10\}\quad D_2=\{4,5,6,7,8,9,10\}$$
Again, one can verify that each draw is in exactly two events. This time, however, $P(B_2\,|\,A_2^c)=\frac 17$
So it is not determined.