Separate impossible, certain and likely
See this course’s project requirements
A chance-model packet with a complete sample space, combined-event calculations, conditional probabilities and a repeated-trial comparison.
Keep your working files in your own notebook or software. Save a private description, checklist, and work link in My Proof.
What to include
- List a complete equal-outcome sample space.
- Calculate a complement and an independent combined event.
- Audit overlap in an inclusive-or event.
- Compare conditional and unrestricted denominators.
- Explain observed frequency versus theoretical chance with all six changed cases.
Review and revise
Use these criteria to check your work and choose what to improve.
- Method: applies the course-specific rules to the supplied cases with visible intermediate work.
- Accuracy: results agree with the stated facts, units, boundaries and independent checks.
- Reasoning: explains why the result follows and identifies a limitation or unresolved question.
- Transfer: completes changed cases and revises the final project when a relevant assumption changes.
Want more background?
The idea in everyday life
Case: a bag contains eight identical-feeling tokens: five blue and three green. One random token is drawn; there are no red tokens.
Probability runs from 0 for an impossible event to 1 for a certain event. A high probability is not a guarantee on one attempt. The complement of an event contains all outcomes in which it does not occur.
Separate impossible, certain and likely — worked practice
Probability runs from 0 for an impossible event to 1 for a certain event. A high probability is not a guarantee on one attempt. The complement of an event contains all outcomes in which it does not occur.
Case: a bag contains eight identical-feeling tokens: five blue and three green. One random token is drawn; there are no red tokens.
Original practice material
Paste at A1.
| AMaterial | BSupplied text |
|---|---|
| Case | Case: a bag contains eight identical-feeling tokens: five blue and three green. One random token is drawn; there are no red tokens. |
Copy as plain text
1. 1. Impossible
State the chance of drawing red.
You should see: 0, because no token is red.
2. 2. Certain
State the chance of drawing blue or green.
You should see: 1, because every token has one of those colors.
3. 3. Likely
Calculate blue and green chances.
You should see: Blue 5/8; green 3/8.
4. 4. Complement
Check the color chances total one.
You should see: 5/8+3/8=1; blue is more likely but not guaranteed.
What to finish
An event/complement probability card with a one-trial uncertainty note.
Watch for this
No red outcome exists in the stated eight-token sample space. Zero here follows from the given contents, not from a small chance.
How can I tell I understand it?
Explain a high-probability changed case without calling its outcome certain.
Quick knowledge check
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