Tree diagrams · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Tree diagrams for combined events

Mathematics · Probability · ages 12-14
Name ______________________   Date ____________

  1. Two dice give 12 equally likely pairs. True or false?

    Circle one:   True   False

  2. A tree diagram for flipping a coin then rolling a die starts with 2 branches. How many branches grow out of each of those, for the die?

    123456
    • 6
    • 2
    • 12

  3. In a tree diagram, you multiply the probabilities along one path to find the probability of that whole path.

    Circle one:   True   False

  4. You spin a spinner with 4 equal sections, then roll a die, and list every pair in a table. How many outcomes are there in total?

    • 12
    • 36
    • 24

  5. A spinner has 3 equal sections: red, blue and green. Spin it, then roll a die. What is P(red then a 6)?

    • 1/9
    • 1/18
    • 1/3
    • 2/9

  6. Listing all 36 dice pairs counts as a sample space diagram. True or false?

    Circle one:   True   False

  7. A coin is tossed 3 times. How many outcomes are in the sample space?

    • 6
    • 3
    • 8
    • 12

  8. A tree splits 1/2 then 1/3 along one path. What is the combined probability?

    • 1/5
    • 1/6
    • 2/6
    • 1/3

  9. A bag has 4 red and 6 blue balls. Draw one and keep it, then draw again. What is P(both red)?

    • 16/100
    • 4/10
    • 1/5
    • 2/15

  10. Omar says the probability of rolling a total of 5 with two dice is 4, because he counted 4 pairs that make 5. What mistake did he make?

    • He should have multiplied the pairs instead of counting them
    • He forgot to divide the number of favourable outcomes by the total number of outcomes
    • He counted the wrong number of pairs
LightMySky · lightmysky.comW1-mt_GDtFU5fyUv-s1

Answer key

For grown-ups. Fold this page away before handing over the rest.

Tree diagrams for combined events W1-mt_GDtFU5fyUv-s1

  1. False · Each of the 6 faces on one die pairs with all 6 faces on the other, so there are 6 x 6 = 36 pairs, not 6 + 6 = 12.
  2. 6 · A die has 6 equally likely faces, so 6 branches grow out of each first branch.
  3. True · That is exactly how branch probabilities combine into a path probability.
  4. 24 · 4 spinner sections times 6 die faces gives 4 × 6 = 24 possible pairs.
  5. 1/18 · 1/3 along the spinner branch times 1/6 along the die branch is 1/18.
  6. True · A full list of pairs is exactly a sample space.
  7. 8 · Each toss has 2 outcomes, so the tree has 2 x 2 x 2 = 8 paths.
  8. 1/6 · 1/2 x 1/3 = 1/6 along the branch path.
  9. 2/15 · 4/10 x 3/9 = 12/90 = 2/15.
  10. He forgot to divide the number of favourable outcomes by the total number of outcomes · Probability is favourable outcomes over total outcomes, so it should be 4/36, which simplifies to 1/9, not 4.
Worksheet · LightMySky