Mathematics 10 — Exercise 12.1 · Q1

Full question

Three fair coins are tossed. Draw a tree diagram and write the sample space of all possible outcomes.

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.

    2×2×2=8
Outcome
('H', 'H', 'H')
('H', 'H', 'T')
('H', 'T', 'H')
('H', 'T', 'T')
('T', 'H', 'H')
('T', 'H', 'T')
('T', 'T', 'H')
('T', 'T', 'T')

Answer

8 outcomes, listed below.

HTHTHTH('H', 'H', 'H')T('H', 'H', 'T')H('H', 'T', 'H')T('H', 'T', 'T')H('T', 'H', 'H')T('T', 'H', 'T')H('T', 'T', 'H')T('T', 'T', 'T')