Tree Diagrams Without Replacement · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

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 even?

    • 5 cards total, 2 even
    • 4 cards total, 1 even
    • 4 cards total, 2 even
    • 5 cards total, 1 even

  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). What is the probability that the two cards drawn without replacement come out odd first, then even?

    • 0.3
    • 0.1
    • 0.6
    • 0.5

  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 both cards are even? 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 the two cards are one odd and one even, in either order?

    • 0.6
    • 0.5
    • 0.4
    • 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, 1 even · Since the card isn't replaced, both the total count and the even count drop by one, because the card removed was itself even.
  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. 0.3 · Follow the odd branch first, then the even branch after the odd card is removed, and multiply.
  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. 0.1 · Multiplying the two branch probabilities along the path gives the chance of both cards being even.
  9. 0.6 · Two routes fit: odd-even 0.3 plus even-odd 0.3 = 0.6.
  10. 0.6 · Two branches fit 'one odd and one even': odd-then-even and even-then-odd. Add those two branches together.
Worksheet · LightMySky