Mathematics 10 — Exercise 12.1 · Q6 (i)

Full question

Two fair six-sided dice are rolled. Draw a tree diagram for the sample space.

Step-by-step solution

  1. Treat choices in order. Each branch at one stage leads to EVERY possible choice at the next stage.

  2. Write one outcome for each complete root-to-leaf path; do not merge differently ordered outcomes.

  3. Multiply the numbers of choices at the stages to count all outcomes.

    6×6=36
Outcome
(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)

Answer

36 outcomes, listed below.

1234561(1, 1)2(1, 2)3(1, 3)4(1, 4)5(1, 5)6(1, 6)1(2, 1)2(2, 2)3(2, 3)4(2, 4)5(2, 5)6(2, 6)1(3, 1)2(3, 2)3(3, 3)4(3, 4)5(3, 5)6(3, 6)1(4, 1)2(4, 2)3(4, 3)4(4, 4)5(4, 5)6(4, 6)1(5, 1)2(5, 2)3(5, 3)4(5, 4)5(5, 5)6(5, 6)1(6, 1)2(6, 2)3(6, 3)4(6, 4)5(6, 5)6(6, 6)