Two dice are rolled together. Ved thinks getting a sum of 2 and getting a sum of 7 are equally…

Why

Ved is treating each POSSIBLE SUM as if it were one equally-likely outcome, the same way each face of a single die is equally likely — but a sum is not one single outcome, it can be reached by several different combinations of the two dice, and different sums have very different numbers of ways to reach them. A sum of 2 can only happen one way: both dice show 1 (1+1). A sum of 7 can happen six different ways: 1+6, 2+5, 3+4, 4+3, 5+2, 6+1 — six separate, equally-likely dice combinations, all adding up to 7. Test it: list out all 36 equally-likely combinations two dice can land on (6 faces on the first die × 6 on the second) — exactly 1 of those 36 gives a sum of 2, while exactly 6 of those 36 give a sum of 7, meaning 7 is six times more likely than 2. His teacher is right: 7 is far more likely than 2 — the number of ways to REACH a sum, not just the sum itself, is what determines its probability.