Finding P(sum = 7) with Two Dice

Pre-Algebra · Axiom Academy

EXAMPLE Finding P(sum = 7) with Two Dice Build the full sample space, count the favorable rolls, and turn that into a theoretical probability. Roll two fair six-sided dice and add the faces. What is the theoretical probability that the sum is 7 , written as ? We will list every possible outcome, count the ones that work, and form the ratio. Nice work. You found a theoretical probability the same way you would for any "equally likely outcomes" problem — count the favorable cases, count the total, divide. Sample space: two dice give equally likely outcomes. Favorable outcomes: exactly 6 rolls sum to 7 — (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) . Order matters: (1,6) and (6,1) are different outcomes, which is why we count 6 pairs rather than 3 . Most likely sum: 7 has more ways to occur than any other sum, so it is the peak of the distribution. Theoretical probability tells you what to expect in the long run: over 60 rolls you would expect about 10 sums of 7 , and over 600 rolls about 100 . Real experiments wobble around that value because of chance.

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