Problem Section 1.2 Exercise 1

Let \(Ω = {a, b, c}\) 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 \(Ω\).

Ans: The eight subsets = 0, {a}, {b}, {c}, {ab}, {ac}, {cb}, {abc}

a <- 1/2
b <- 1/3
c <- 1/6
a
## [1] 0.5
b
## [1] 0.3333333
c
## [1] 0.1666667
0
## [1] 0
a*b
## [1] 0.1666667
a*c
## [1] 0.08333333
b*c
## [1] 0.05555556
a*b*c
## [1] 0.02777778