AP Syllabus focus:
‘Pedigrees and probability equations, such as P(A or B) and P(A and B), help predict genotypes and phenotypes.’
Pedigrees translate family history into genetic predictions. By combining careful symbol-based interpretation with core probability rules, you can infer likely genotypes, identify carriers, and estimate the chance of specific offspring phenotypes.
Pedigrees as genetic models
A pedigree is a simplified model of inheritance across generations, where individuals are connected by mating lines and descent lines.
Standard pedigree symbols provide a shared “language” for encoding sex, relationships, and trait status in a family tree. Using a consistent legend (e.g., squares/circles for sex, shading for affected status, and special markings for carriers) makes it possible to translate family structure into genotype and phenotype inferences. Source
Pedigree: A diagram that tracks the inheritance of a trait through multiple generations using standardized symbols for sex, relationships, and trait status.
Pedigrees are used to predict genotypes (allele combinations) and phenotypes (observable traits) when not all genotypes are directly observable.
What information a pedigree provides
Trait status of individuals (affected vs unaffected) based on shading/marking
Family structure (who produced which offspring)
Generational patterning, which can support genotype inference
Constraints that rule out impossible genotypes (e.g., an affected child requires transmission from parents under many models)
Standard reasoning steps (no calculations yet)
Identify which individuals’ genotypes are certain from the pedigree (sometimes only a few are fixed).
Assign possible genotypes to others using allele logic and family relationships.
Use probability to compare remaining possibilities and predict:
the chance a person is a carrier
the chance future offspring are affected or unaffected
Core genotype ideas used in pedigrees
Pedigree probability problems often depend on whether an individual can “hide” an allele while showing a different phenotype.
Carrier: An individual who has a disease-associated allele but does not show the associated phenotype (commonly a heterozygote for a recessive allele).
Even without naming a specific inheritance pattern, pedigree logic often relies on these general principles:
Offspring receive one allele from each parent for a gene.
If an allele can be present without changing phenotype, unaffected individuals may still transmit it.
Some genotype assignments become fixed once you know the genotypes or phenotypes of close relatives.
Probability language for pedigrees
In pedigree problems, define each uncertain outcome as an event (e.g., “the mother is a carrier,” “the child is affected”). Then apply probability rules to combine events across individuals or across reproductive outcomes.
Common event types:
Independent events: one outcome does not change the probability of the other (often assumed for different offspring events under the same parental genotypes).
Dependent events: one outcome changes the probability of the other (common when learning new pedigree information changes the likelihood of a parent’s genotype).
Probability equations used in pedigree predictions
Use “and” for joint outcomes and “or” for alternative outcomes.
A probability tree diagram organizes multi-step outcomes so each branch represents a conditional probability (e.g., ) given what happened earlier. The probability of a complete path corresponds to a joint event (an intersection) and is found by multiplying along the path, matching . Source
= event A occurs (unitless probability)
= event B occurs (unitless probability)
= probability of event B occurring given that A has occurred (unitless probability)
= overlap where both events occur (unitless probability)
These equations support two major pedigree tasks:
Combining sequential conditions (use “and,” often via multiplication with conditional probability).
Adding alternative pathways to the same outcome (use “or,” while avoiding double-counting overlap).
Applying probability to pedigree-based predictions
When to use “and” (multiplication logic)
Use when multiple requirements must all be true to get an outcome, such as:
a parent has a particular genotype and passes a specific allele
two parents each transmit a required allele and the child inherits the needed combination
Key idea: when information updates genotype likelihoods, treat later steps as conditional on earlier ones.
When to use “or” (addition logic)
Use when an outcome can occur through different, alternative routes, such as:
an unknown genotype could be one of two possibilities that both lead to the same child phenotype
a phenotype could result from more than one parental genotype pairing consistent with the pedigree
Typical sources of dependency in pedigrees
Knowing one child’s phenotype can change the probability a parent is a carrier.
Knowing one sibling’s genotype can change probabilities for another sibling if parental genotypes become constrained.
Additional pedigree information should trigger re-evaluation of earlier assumptions using conditional probability.
FAQ
Treat “carrier” as event $A$ and “unaffected child” as event $B$, then update using conditional probability: compare $P(B|A)$ to $P(B|\text{not }A)$. Renormalise so updated probabilities sum to 1.
They are independent only after conditioning on fixed parental genotypes. If parental genotypes are uncertain, siblings’ outcomes provide shared information, so probabilities become dependent until you condition on each genotype case.
Introduce events for each unknown (e.g., “individual is affected”) and carry multiple genotype scenarios forward. Use $P(A \text{ or } B)$ to combine mutually exclusive scenarios, weighting by how consistent each is with observed relatives.
Adding two pathways that are not mutually exclusive (both can happen) without subtracting $P(A \cap B)$. This inflates the final probability beyond the true value.
Define events as biological checkpoints:
genotype state (e.g., “is a carrier”)
transmission (e.g., “passes the allele”)
resulting phenotype
Then combine checkpoints with “and,” and combine alternative genotype pathways with “or.”
Practice Questions
In a pedigree, two unaffected parents have an affected child. State what this suggests about the parents’ genotypes, and justify your answer using allele transmission logic. (2 marks)
Both parents are likely carriers/heterozygous for an allele associated with the trait (1)
An affected child must receive the relevant allele from each parent, so each parent must be able to transmit it despite being unaffected (1)
Describe how pedigrees and probability equations can be used together to predict (i) an individual’s genotype and (ii) the probability of an offspring phenotype. Your answer must refer to and . (5 marks)
Pedigree used to assign certain vs possible genotypes based on family relationships and trait status (1)
Define events (e.g., “parent is a carrier,” “offspring inherits allele”) and link them to genotype/phenotype outcomes (1)
Use (multiplication/conditional form) to combine required steps for an outcome, such as genotype condition and transmission (1)
Use to add alternative genotype pathways that can produce the same outcome, subtracting overlap to avoid double counting (1)
Explain dependency/conditional probability arising when new pedigree information changes genotype probabilities (1)
