Safety, privacy and evidence boundary
Use fictional organisms, coins/cards, and published-style datasets. Do not require personal family histories, ancestry testing, fertility information, medical pedigrees, or personal genetic data. Trait inheritance never ranks human worth.
Explicit science instruction
The product rule multiplies probabilities for events that must both occur when the relevant events are independent or conditionally specified. The sum rule adds probabilities for mutually exclusive alternative outcomes.
Genetic reasoning must state assumptions about independence. Linked loci violate simple independent-assortment assumptions, and conditional information can change probabilities.
Vocabulary: product rule; sum rule; independent; mutually exclusive; conditional probability; outcome.
Worked example with reasoning
If two independently assorting loci each have a 1/2 probability of contributing a specified allele, the joint probability is 1/2 × 1/2 = 1/4. If a phenotype can arise from either of two mutually exclusive genotypes with probabilities 1/4 and 1/2, total probability is 3/4.
Guided question
Why must you check independence before multiplying probabilities?
Independent work
- Solve three product-rule examples.
- Solve two sum-rule examples.
- Identify one linked-locus case where simple multiplication is unsafe.
- Write assumptions beside each calculation.
Misconception check
Multiplying any two numbers associated with genetics is not the product rule; the events and conditioning must be defined.
Formative understanding check
If independent events have probabilities 1/2 and 1/4, what is the probability both occur?
Worked response
1/8.
Open-book formative practice only; not an official mastery attempt or grade.
Mentor evidence conference
Ask Archaemenes to challenge your probability, evidence classification, model assumptions, and limitations. The mentor does not infer personal genetics or provide protected assessment answers.
Open ArchaemenesTeacher guidance
Foundation: use event trees. Core: justify the rule chosen for each problem. Extended: compare direct enumeration, tree diagrams, and probability rules for the same cross.
Preserve learning evidence
Keep models, calculations, corrections, and limitations in the matching Week 21 evidence field.
Return to evidence workspace