Combine independent events
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.
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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: two independent fair coins are tossed. Complete space: HH, HT, TH, TT.
Events are independent when learning that one occurred does not change the probability of the other. For independent events, the chance of both is the product. Independent is different from mutually exclusive: independent events can occur together.
Combine independent events — worked practice
Events are independent when learning that one occurred does not change the probability of the other. For independent events, the chance of both is the product. Independent is different from mutually exclusive: independent events can occur together.
Case: two independent fair coins are tossed. Complete space: HH, HT, TH, TT.
Original practice material
Paste at A1.
| AMaterial | BSupplied text |
|---|---|
| Case | Case: two independent fair coins are tossed. Complete space: HH, HT, TH, TT. |
Copy as plain text
1. 1. Single
Find the chance each separate coin is heads.
You should see: Each is 1/2.
2. 2. Both
Find the outcomes with two heads.
You should see: HH only, probability 1/4.
3. 3. Multiply
Compare with the independence rule.
You should see: 1/2×1/2=1/4.
4. 4. Distinguish
Explain why heads on coin 1 and heads on coin 2 are not mutually exclusive.
You should see: They occur together in HH.
What to finish
An independent-event calculation and comparison with a dependent draw.
Watch for this
Removing a token changes the bag composition. Use the updated conditional probability rather than assuming independence.
How can I tell I understand it?
Recognize when a changed draw mechanism invalidates the independent product.
Quick knowledge check
Answer all 3 questions. Get at least 2 right and the lesson completes automatically.
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Answer all 3 questions above and get at least 2 right. You can review the explanations and try again.
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Source & access notes · checked 2026-10-01
Web open/search showed the official page, its topic heading and relevant concept description. This is a content/source check, not a provider endorsement.
Access: Official page retrieved with the web reader on 2026-10-01; interactive tools and videos were not certified by retrieval.
Reuse: Original fictional teaching cases, calculations, questions and examples; link and short factual paraphrase only. No copied source exercises or illustrations.
Source & access notes · checked 2026-10-01
Web open/search showed the official page, its topic heading and relevant concept description. This is a content/source check, not a provider endorsement.
Access: Official page retrieved with the web reader on 2026-10-01; interactive tools and videos were not certified by retrieval.
Reuse: Original fictional teaching cases, calculations, questions and examples; link and short factual paraphrase only. No copied source exercises or illustrations.
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