Let $A_1,A_2,A_3,A_4$ be events such that for every $i,j,k=1,2,3,4$,
$P(A_i) = \frac{1}{2}$,
$P(A_i \cap A_j)= \frac{1}{3},\quad i\ne j$,
$P(A_i\cap A_j\cap A_k) = \frac{1}{4},\quad i\ne j, j\ne k, k\ne i$,
$P(A_1\cap A_2\cap A_3\cap A_4) = \frac{1}{5}$.
Find $P(A^c_1\cap A^c_2\cap A^c_3)$.
Progress: I have obtained $$P( A_1 \cup A_2 \cup A_3 \cup A_4) = \frac{4}{5}$$
Any clues on how I can find the intersection of the complements? Thanks!