Tree Diagrams Without Replacement · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.
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Trees when nothing goes back

Mathematics · Probability · ages 15-16
Name ______________________   Date ____________

  1. A bag has 5 cards numbered 1 to 5. Sam draws one card and it shows a 2, then sets it aside (no replacement). For the second draw, how many cards are left in the bag, and how many of them are odd?

    • 5 cards total, 3 odd
    • 4 cards total, 2 odd
    • 4 cards total, 3 odd
    • 3 cards total, 3 odd

  2. In a tree without replacement, what must you do to the second stage?

    • Rebuild it from what is left
    • Keep it the same
    • Drop the second stage

  3. In a tree diagram, the branches leaving one point always add to 1.

    Circle one:   True   False

  4. Cards 1 to 5. One even card is drawn and set aside. How many even cards are left?

    Answer: ______________

  5. Same 5-card bag (numbered 1 to 5). Two cards are drawn without replacement. What is the probability that the 5 is drawn both times?

    • 0.2
    • 0.04
    • 0.05
    • 0

  6. Cards 1 to 5, two drawn without replacement. What is P(odd then even)?

    • 0.1
    • 0.6
    • 0.3

  7. Cards 1 to 5. One odd card is drawn and set aside. What is P(odd) on the second draw?

    • 3/5
    • 2/4
    • 3/4

  8. A bag has 5 cards numbered 1 to 5. Priya draws two cards without replacement. What is the probability that the first card is the 1 and the second card is the 5? Give your answer as a decimal.

    Answer: ______________

  9. Cards 1 to 5, two drawn without replacement. What is P(one odd and one even, in either order)?

    • 0.6
    • 0.3
    • 0.4

  10. Same 5-card bag (numbered 1 to 5), two cards drawn without replacement. What is the probability that at least one of the two cards is even?

    • 0.3
    • 0.4
    • 0.7
    • 0.9
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Answer key

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

Trees when nothing goes back W1-mt_NfiAY_wMwZ-s1

  1. 4 cards total, 3 odd · The card removed was even, so the total drops by one but the number of odd cards stays at 3.
  2. Rebuild it from what is left · The removed item is gone, so the second-stage probabilities must be rebuilt.
  3. True · The branches cover every outcome from that point, so they total 1.
  4. 1 · Two evens minus the drawn one leaves 1 even card.
  5. 0 · Once the 5 is drawn it is out of the bag, so the second-stage branch for '5 again' has probability 0/4 = 0.
  6. 0.3 · Along the route: 3/5 times 2/4 = 6/20 = 0.3.
  7. 2/4 · Two odds remain out of 4 cards, so the rebuilt fraction is 2/4.
  8. 0.05 · Multiply the two branch probabilities along the path: 1/5 for the 1, then 1/4 for the 5 from the four cards left.
  9. 0.6 · Two routes fit: odd-even 0.3 plus even-odd 0.3 = 0.6.
  10. 0.7 · The only branch with no even card is odd then odd, 3/5 x 2/4 = 0.3. Every other branch fits, so P(at least one even) = 1 - 0.3 = 0.7.
Worksheet · LightMySky