Let ? = {a, b, c} be a sample space. let m(a) = 1/2, m(b) = 1/3, and m(c) = 1/6. find the probabilities for all eight subsets of ? .

A= {a,b,c} . Since this set has 3 elements, the number
of its total subset is 2³ = 8 (including the Ф element):

Here below all the subsets of {a,b,c}, with their related probabilities, knowing that P(a) = 1/2 ; P(b) = 1/3 and P(c) = 1/6

{a}        →→→→1/2
{b}        →→→→1/3
{c}        →→→→1/6
{a,b}     →→→→1/2 + 1/3 =  5/6
{a,c}     →→→→1/2 + 1/6  =  2/3
{b,c}     →→→→1/3 + 1/6  =  1/2
{a,b,c}  →→→→1/2 + 1/3 + 1/6 = 1
{∅}       →→→→0 =0