Step-by-step explanation:
there are 2 spinner and 6 die possibilities, so there are 2×6 = 12 different outcomes overall.
but only 2 of these outcomes have unique sums :
2+1 = 3
3+6 = 9
no other combination can create these sums.
the other 10 outcomes have only 5 different sums :
4, 5, 6, 7, 8
(2+2 = 3+1, 2+3 = 3+2, 2+4 = 3+3, 2+5 ÷ 3+4, 2+6 = 3+5)
so, we have 2 + 5 = 7 different sums.
but they have different probabilities !