 Solution

ID: past-exam-of-the-year-1-of-the-computer-science-course-of-the-university-of-oxford/2014/discrete-mathematics-continuous-mathematics-and-probability/7/a/iii/solution

Mutual independence means that for every nonempty

I \subseteq {1, 2, 3}

P (i \in I ⋂ A_{i}) = i \in I \prod P (A_{i}) .

Beyond the trivial single-event identities, this requires the three pairwise equalities and the triple equality

P (A_{1} \cap A_{2} \cap A_{3}) = P (A_{1}) P (A_{2}) P (A_{3})

. Pairwise independence alone omits that last requirement.

 New to topics? Read the docs here!