Let \(\Omega\) = (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 \(\Omega\).
Christian’s Response:
To identify all eight subsets, we’ll use this formula:
m(A) = \(\Sigma\)m(w)
The formula tell us to add the probabilities of all the outcomes for our sample space \(\Omega\). When we use the formula, we get all eight outcomes:
m(\(\emptyset\)) = 0
m({a}) = 1/2
m({b}) = 1/3
m({c}) = 2/6
m({a+b}) = 5/6
m({a+c}) = 2/3
m({b+c}) = 1/2
m(\(\Omega\)) = 1