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

Experimental vs Theoretical Probability

Mathematics · Probability · ages 10-11
Name ______________________   Date ____________

  1. A fair die is rolled 60 times. How many of each number are expected?

    Answer: ______________

  2. A fair die is rolled 60 times. About how many times do you expect a 4?

    • 10
    • 60
    • 4
    • 6

  3. If you roll a fair die 60 times, what is the theoretical (expected) number of times each number should appear?

    • 6
    • 10
    • 60

  4. Leo rolls a fair six-sided die 60 times and tallies these counts: 8, 11, 9, 13, 7, 12. Are these experimental results, or a theoretical prediction?

    • Experimental results, counted from real rolls
    • A theoretical prediction, worked out before rolling
    • The expected counts for a fair die, which are all 10

  5. A fair six-sided die is rolled 600 times. About how many 6s are expected?

    Answer: ______________

  6. This chart shows the results of 60 die rolls. Which number's count is closest to the theoretical prediction of 10?

    192153741051267
    • Number 1
    • Number 2
    • Number 4

  7. A class rolls a fair six-sided die 60 times and gets twelve 6s instead of the expected ten. What best explains this?

    • The die must be unfair
    • They rolled it wrongly
    • Exactly ten sixes is never promised; small wobbles are normal
    • Expected means guaranteed

  8. Rolling a fair die, Dev says a share from 600 rolls tends to sit closer to one sixth than a share from 60 rolls, even though one run of 600 can still land further off. Is Dev right?

    Circle one:   True   False

  9. Mia flips a fair coin 10 times and gets 8 heads. She says, 'Heads must be more likely than tails.' What is wrong with her thinking?

    • With only 10 flips, results can look uneven just by chance; more flips would likely even out closer to 50:50
    • Nothing, she is right
    • She needs to flip a different coin

  10. Class A rolls a fair six-sided die 60 times and gets 8 sixes. Class B rolls it 600 times and gets 96 sixes. Whose share of sixes is nearer the theoretical one sixth, and why?

    • Class A, because fewer rolls are fairer
    • Both exactly, because expected means exact
    • Class A, because 8 is nearer 10 than 96 is to 100
    • Class B, because 96 in 600 is nearer one sixth
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Answer key

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

Experimental vs Theoretical Probability W1-mt_-bMnJcPJy8-s1

  1. 10 · 60 rolls split over 6 faces gives 10 of each number.
  2. 10 · Each face expects one sixth of the rolls: 60 divided by 6 = 10.
  3. 10 · 60 rolls shared evenly across 6 numbers is 60 divided by 6, which is 10 each.
  4. Experimental results, counted from real rolls · These are real counts from rolling the die, so they are experimental results. A theoretical prediction is worked out before rolling, and it would put the expected count at 10 for every face.
  5. 100 · One sixth of 600 is 100 sixes expected.
  6. Number 4 · Number 4 came up exactly 10 times, matching the expected 10. Number 2 was the furthest off, showing up 15 times instead of about 10.
  7. Exactly ten sixes is never promised; small wobbles are normal · Twelve against an expected ten is ordinary wobble in 60 rolls, so it does not show the die is unfair.
  8. True · Dev is right. Bigger samples average out lucky streaks, so their shares usually sit nearer one sixth, and that is a tendency rather than a promise.
  9. With only 10 flips, results can look uneven just by chance; more flips would likely even out closer to 50:50 · Small numbers of trials often look uneven even with a fair coin. Flipping many more times usually brings the results closer to the true 50:50 chance.
  10. Class B, because 96 in 600 is nearer one sixth · Class B: 96 in 600 is 16.0 percent, which sits nearer one sixth (16.7 percent) than 8 in 60 at 13.3 percent.
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