Two dice with faces numbered from 1 to 6 are rolled together. What are the possible sums? Which of these sums has the maximum probability?

Question

Philoid · Accepted Answer

Sample space of two dice rolled together:

(1, 1) (1, 2) (1, 3) (1, 4) (1, 5) (1, 6)

(2, 1) (2, 2) (2, 3) (2, 4) (2, 5) (2, 6)

(3, 1) (3, 2) (3, 3) (3, 4) (3, 5) (3, 6)

(4, 1) (4, 2) (4, 3) (4, 4) (4, 5) (4, 6)

(5, 1) (5, 2) (5, 3) (5, 4) (5, 5) (5, 6)

(6, 1) (6, 2) (6, 3) (6, 4) (6, 5) (6, 6)

Maximum sum will be 12 and minimum will be 2

Sum (2) – {(1, 1)} = 1

Sum (3) – {(1, 2) (2, 1)} = 2

Sum (4) – {(1, 3) (2, 2) (3, 1)} = 3

Sum (5) – {(1, 4) (2, 3) (3, 2) (4, 1)} = 4

Sum (6) – {(1, 5) (2, 4) (3, 3) (4, 2) (5, 1)} = 5

Sum (7) – {(1, 6) (2, 5) (3, 4) (4, 3) (5, 2) (6, 1)} = 6

Sum (8) – {(2, 6) (3, 5) (4, 4) (5, 3) (6, 2)} = 5

Sum (9) – {(3, 6) (4, 5) (5, 4) (6, 3)} = 4

Sum (10) – {(4, 6) (5, 5) (6, 4)} = 3

Sum (11) – {(5, 6) (6, 5)} = 2

Sum (12) – {(6, 6)} = 1

Sum of 6 has maximum possibility because it has more number of outcomes.