AP Syllabus focus:
‘Rules of probability predict the likelihood that particular alleles, and therefore single-gene traits, will be passed to offspring.’
Probability provides a precise way to predict inheritance patterns from meiosis and fertilisation. In single-gene crosses, allele segregation creates measurable chances for specific gametes, genotypes, and phenotypes in offspring.
Probability basics for single-gene inheritance
Events, outcomes, and genetic “chance”
Probability: The likelihood that a particular outcome will occur, expressed from 0 (impossible) to 1 (certain).
In genetics, an event might be “a gamete carries allele A” or “an offspring is aa.” Probabilities are built from the possible outcomes of allele segregation and random fertilisation.
Independent vs. dependent events
Independent events: Two events where the occurrence of one does not change the probability of the other.
Practice Questions
FAQ
Dependence is relevant when one outcome changes the sample space for the next outcome.
Examples include:
Sampling without replacement from a very small set of gametes (a contrived situation)
Any explicit constraint such as “one child is known to be affected”
In typical fertilisation predictions, allele contribution from each parent is treated as independent.
Conditional probability is used when new information is given (e.g., an offspring already shows a phenotype). You update the probability space to include only outcomes consistent with that information.
Formally: $P(A\mid B)=\dfrac{P(A\text{ and }B)}{P(B)}$.
A Punnett square enumerates all equally likely gamete combinations, while probability rules compute the same totals algebraically.
They agree when:
Gamete types are correctly assigned probabilities
Each fertilisation outcome is appropriately counted once
Assumptions of random fertilisation and fair segregation hold
If segregation is distorted, the gamete probabilities are not $0.5$ and $0.5$. You still use the same AND/OR/complement rules, but with the altered gamete probabilities (for example, $P(A)=0.6$, $P(a)=0.4$). The structure of the calculation remains the same; only the inputs change.
Use OR when you can list a small number of mutually exclusive outcomes that lead to the result.
Use the complement rule when:
The desired outcome is “at least one”
There are many ways to achieve it
The “none” case is simpler to express and compute
