The following probabilities have been assigned to various subsets of the sample space S.

A= (0.05, 0.10, 0.10, 0.15)
B= (0.05, 0.10, 0.10, 0.15)
C= (0.05, 0.05, 0.10, 0.175)
a. Are the three events A, B and C pairwise-independent events?

A is independent of B or not? P(A)=0.40 P(B)=? so, we want to test P(A∩B)=P(A)*P(B) condition has to hold for those events to have a pair-wise independence. If P(A∩B)=0.20, then P(A)*P(B) = 0.16, that tells that these events are not independent.
B is independent of C or not? Focus on probabilities assigned in the subsets, 0.05 is repeated in C, but 0.10 is repeated in B, so P(A∩C)=?
A is independent of C or not?