Multi-step experiments and independence
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Log in to continueDescribe complete two- and three-step sample spaces and calculate events with changing or unchanged probabilities.
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A bag contains 3 red and 2 blue counters. Three random draws each replace and remix the counter. Find P(red, then blue, then red).
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Answer: 18/125
- With replacement, branch probabilities stay 3/5, 2/5, 3/5.
- Multiply the three independent probabilities to get 18/125.
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Curriculum reference
Victorian Curriculum F–10 Version 2.0
Pi Leo practice scope
Describe complete two- and three-step sample spaces and calculate events with changing or unchanged probabilities.
Read the official VCAA curriculum description (VC2M10P02)
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- Supported by the guided activity; selecting an MCQ does not demonstrate this action.
- Supported by the guided activity; selecting an MCQ does not demonstrate this action.
- VC2M10P02-C01Multiply probabilities along a specified independent sequence.
- VC2M10P02-C02Describe full two- and three-step outcome spaces and combined events.
- VC2M10P02-C03Use conditional probabilities at each stage.
- VC2M10P02-C04Investigate independence by comparing conditional and unconditional probabilities.
- VC2M10P02-C05Apply and explain multi-step experiments and independence using read and connect representations.
- VC2M10P02-C06Apply and explain multi-step experiments and independence using calculate and explain each step.
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Subskills
These practice subskills map to the curriculum topic. Guided activities cover skills beyond multiple-choice questions.
Descriptor-derived subskills
- D01Replacement can restore the same probabilitiesMultiply probabilities along a specified independent sequence.
- D02Without replacement changes the modelUse conditional probabilities at each stage.
- D03Read and connect representationsApply and explain multi-step experiments and independence using read and connect representations.
- D04Calculate and explain each stepApply and explain multi-step experiments and independence using calculate and explain each step.