For example, for n = 4 and the outcome hT, T, H, Hi, the events A 1,3 , A 1,4 , A 2,3 , and A 2,4…
For example, for n = 4 and the outcome hT, T, H, Hi, the events A1,3, A1,4, A2,3, and A2,4 all occur; A1,2 and A3,4 do not. Thus, from n independent coin flips, we’ve defined Ω(n 2 ) different events— n 2 , to be specific. In the next few exercises, you’ll show that these n 2 events are pairwise independent, but not fully independent
1. 
2. 8 Let i and j > i be arbitrary, and let i ′ and j ′ > i ′ be arbitrary. Show that any two distinct events Ai,
and Ai ′ ,j ′ are independent. That is, show that Pr Ai,j |Ai ′ ,j ′ = Pr Ai,j |Ai ′ ,j ′ = 1 2 if {i, j} 6= {i ′ , j ′
