↓ die 1 → die 2
Show me:
The event — at least one 6
11/36
11 shaded cells — fiddly!
The complement — no 6 at all
25/36
a clean 5×5 block
They add to
1
11/36 + 25/36 = 36/36
Hard way: count 11 scattered cells → 11/36.
Easy way: P(at least one 6) = 1 − P(no 6) = 1 − 25/36 = 11/36. Same answer, far less counting.
"At least one" is a nightmare to count head-on — the winning cells are scattered. But its complement, "none", is a tidy block. Count the easy one, then do 1 − that. The complement is sometimes far easier to count.