Question

Two dice are rolled. What is the theoretical probability that the sum is 5? Answer: 1/9. Is the answer wrong? (No brute force explanations are preferable.)

Answer 1

Since 5 = 1 + 4 or 3 + 2
=> 2 * 2 = 4 choices
P = 4/ 36 = 1/9

Answer 2

Look at the chart of the 6 times 6 or 36 possible outcomes of tossing a pair of dice. Ignore the red and blue markings. Look for the right to left diagonal of the chart where the sums of 5 lie. You will see (1,4) and (2,3) and (3,2) and (4,1). Those are four of the 36 ways the pair of dice can land. So, the probability of tossing a sume of 5 = 4/36 which simplifies to 1/9.