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Sample Spaces: Lists, Tables & Tree Diagrams — Mixed

Every first-stage branch splits into all the second-stage outcomes. Count the ends.

ExampleYou spin or throw a coin (heads or tails) and then a spinner (four equal sections).
The tree diagram below has the first stage drawn. Complete it, list the whole sample space, and find P(T, 4).
HH, 1H, 2H, 3H, 4TT, 1T, 2T, 3T, 4 The first stage has 2 branches and each splits into 4, so the sample space has 2 × 4 = 8 outcomes:
H, 1 · H, 2 · H, 3 · H, 4 · T, 1 · T, 2 · T, 3 · T, 4
Each is equally likely, so P(T, 4) = 18. A tree makes the multiplication visible — every branch of stage one carries a full copy of stage two.
  1. 1.You spin or throw a coin (heads or tails) and then a die (six faces).
    The tree diagram below has the first stage drawn. Complete it, list the whole sample space, and find P(T, 3).
    HH, 1H, 2H, 3H, 4H, 5H, 6TT, 1T, 2T, 3T, 4T, 5T, 6
  2. 2.You use a spinner (three equal colors) and a spinner (three equal colors).
    Write an organized list of every outcome. How do you know you have not missed one?
  3. 3.You use a spinner (three equal colors) and a spinner (three equal colors).
    Fill in the table so every cell holds one outcome. How many outcomes are there, and why does the table have that many cells?
    redbluegreen
    red
    blue
    green
  4. 4.You use a spinner (four equal sections) and a spinner (three equal colors).
    Write an organized list of every outcome. How do you know you have not missed one?
  5. 5.You spin or throw a spinner (three equal colors) and then a coin (heads or tails).
    The tree diagram below has the first stage drawn. Complete it, list the whole sample space, and find P(red, H).
    redred, Hred, Tblueblue, Hblue, Tgreengreen, Hgreen, T