Events a, b, and c in a sample space have p(a)=0.2, p(b)=0.4, and p(c)=0.1. find p(a ∪ b ∪ c. if a and b are mutually exclusive, a and c are independent, and b and c are independent.

If and are mutually independent, then and .

If and are independent, then . Ditto for and .

The inclusion/exclusion principle says that



Since and are mutually exclusive, their intersection is the empty set. It then follows that also is the empty set, so the last probability is also 0.

Plug in what we know:

X=3 and y=4 is the answer