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Grade 11 · unit review

Review: Count Carefully in Probability Models

Use two-way counts, conditional sample spaces, independence tests, and updated draws.

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Bring the unit skills together

Use these 4 new cases to check your reasoning. Choices are temporary and are not saved to an account, sent to staff or recorded as school grades. Download your current review choices before leaving or reloading.

Unit review questions
1. A uniform box has red circle 5, red noncircle 3, blue circle 7, blue noncircle 9. Given circle, what is P(red)?
2. A uniform box has red circle 3, red noncircle 7, blue circle 2, blue noncircle 8. What is P(red and circle)?
3. A uniform box has red circle 2, red noncircle 6, blue circle 3, blue noncircle 9. Are red and circle independent?
4. A box has 5 red and 3 blue cards. Two are drawn without replacement. What is P(red then blue)?

The download contains your current choices and any checked feedback. Keep the separate transfer-task work in your own document; downloading its instructions does not mark it complete.

Use the skills in a new task

Audit a fictional uniform card box with red circle 3, red noncircle 7, blue circle 5, blue noncircle 5. Show row and column totals. Find P(red and circle) and P(red given circle), then test independence of red and circle. Separately find the chance of two reds drawn without replacement from this box. State each denominator and its sample space.

Work on paper or in your own document. Explain the choices you made.

  • Find 20 total, 10 red, 10 blue, 8 circle, and 12 noncircle.
  • Use 3/20 for red and circle and 3/8 for red given circle.
  • Compare 3/8 with 10/20 to show dependence.
  • Use (10/20)(9/19) = 9/38 for two reds without replacement.
  • Explain all 20, conditioned 8, and updated 19 as distinct allowed sets.
Compare with a model response

The table totals are red 10, blue 10, circle 8, noncircle 12, grand total 20. P(red and circle) = 3/20; P(red given circle) = 3/8. Since 3/8 differs from P(red) = 1/2, the attributes are dependent. Two reds without replacement has chance (10/20)(9/19) = 9/38; removing one red changes the second sample space to nineteen.

A different response can also meet the criteria. Compare the evidence and reasoning, rather than copying the wording.