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”

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

For many AP Biology single-gene problems, the allele a parent contributes in one gamete is treated as independent of what the other parent contributes at fertilisation. Independence is what allows multiplication of probabilities across parents.

Core probability rules used in inheritance

Genetic predictions commonly rely on the multiplication (AND) rule, the addition (OR) rule, and the complement rule.

These rules let you translate segregation and fertilisation into predicted genotype or phenotype likelihoods without needing to list every possibility.

The multiplication rule (AND) in genetics

Use AND when multiple conditions must happen together, such as:

• A parent produces a gamete with a specific allele and the other parent produces a gamete with a specific allele.

• An offspring must inherit a particular allele from the mother and a particular allele from the father.

Key idea: multiplying probabilities assumes the events are independent (common when combining parental contributions at fertilisation).

The addition rule (OR) and mutually exclusive outcomes

Use OR when there are multiple alternative ways to obtain the same result, such as:

• An offspring genotype that could arise from more than one gamete combination.

• A phenotype that results from more than one genotype (for example, a dominant phenotype from either homozygous dominant or heterozygous genotypes).

If the alternatives cannot happen at the same time (they are mutually exclusive), then $P(A\text{ or }B)=P(A)+P(B)$ because $P(A\text{ and }B)=0$. In inheritance, “offspring is AA” and “offspring is Aa” are mutually exclusive outcomes for a single child.

The complement rule (NOT) for “at least one”

The complement is especially useful for statements like “at least one offspring shows the recessive phenotype.” Instead of adding many separate cases, you often find:

• Probability of none showing the phenotype

• Then subtract from 1 to get “at least one”

This approach is powerful when the number of offspring is large or when multiple outcomes would be tedious to enumerate.

Connecting probability to allele segregation

Gamete probabilities come from segregation

During meiosis, alleles of a gene separate so each gamete receives one allele.

This diagram summarizes the major stages of meiosis (I and II), highlighting how one diploid cell produces four haploid gametes. It reinforces the mechanistic basis for segregation: each gamete receives only one allele per gene after homologous chromosomes (meiosis I) and sister chromatids (meiosis II) separate. Source

For a heterozygote, segregation produces two gamete types in equal proportions (a 1:1 probability split), assuming fair segregation and no selection.

For a homozygote, all gametes carry the same allele (probability 1 for that allele).

Zygote probabilities combine two independent gamete draws

Fertilisation can be treated as a random union of one gamete from each parent. In probability terms:

• Choose an allele from parent 1 (based on that parent’s gamete probabilities)

• Choose an allele from parent 2

• Combine them to form an offspring genotype

When you need the probability of a specific genotype, you often:

• Use multiplication to combine the required parental contributions (AND)

• Use addition if there are multiple gamete pairings that produce the same genotype (OR)

Phenotype probabilities depend on genotype-to-phenotype rules

Single-gene traits often involve dominance, where different genotypes may map to the same phenotype.

This figure contrasts phenotype vs. genotype outcomes for a classic single-gene Mendelian scenario, showing how offspring genotypes (e.g., $YY$, $Yy$, $yy$) translate into phenotype proportions. It visually reinforces why phenotype prediction can require summing multiple genotype probabilities (an “OR” calculation) when more than one genotype produces the same phenotype. Source

Then phenotype prediction becomes a probability “OR” problem:

• Add probabilities of all genotypes that yield the phenotype of interest

• Or use the complement rule to compute “not that phenotype” and subtract from 1

Common pitfalls in AP Biology probability problems

• Confusing OR with AND: “offspring is Aa” requires a specific allele from each parent (AND), not an alternative (OR).

• Forgetting to subtract overlap in the general OR rule: if outcomes can occur together, use $P(A)+P(B)-P(A\text{ and }B)$.

• Treating non-independent events as independent: independence is typically valid when combining parental gametes at fertilisation, but dependence can arise within a single parent’s set of gametes under special constraints.

• Mixing up probability and expected ratio: ratios summarise typical outcomes over many offspring; probability describes the chance for a single offspring.