Probability in Monohybrid Crosses

Under Mendelian segregation, each heterozygous parent produces A and a gametes with probability 1/2. With random fertilization, the combinations AA, Aa, aA and aa each have probability 1/4. The two heterozygous combinations Aa and aA describe the same genotype and are combined. This gives the genotype ratio 1 AA : 2 Aa : 1 aa. The probabilities sum to one. A Punnett square displays the same four combinations, while the calculation makes the probability factors and grouping explicit. Each combination has the same probability.

With complete dominance, both AA and Aa show the dominant phenotype; only aa shows the recessive phenotype. The 1:2:1 genotype ratio therefore becomes three dominant combinations and one recessive, giving 3:1. This result assumes a fully dominant allele. With incomplete dominance or codominance, heterozygous offspring can look different and the phenotype ratio changes. Genotype ratio is a separate statement about allele combinations and should be reported separately from the observable trait. Group the four Punnett-square cells by phenotype to obtain that ratio.

The simple cross describes one autosomal locus with two alleles, heterozygous parents, Mendelian segregation, random fertilization and equally likely gametes. It also assumes genotypes survive equally before observation and no other influence changes the trait. Sex-linked inheritance, linkage, segregation distortion, selection or variable penetrance require another model. State the assumptions alongside the ratio in coursework or a report. This makes clear which conditions support the 1:2:1 result. The model tracks alleles at the specified locus. Verify the inheritance pattern at the stated locus.

The 1/4 is the probability for each conception under the model. For four offspring, one aa child is the expected count, but the observed number can be zero, one, two, three or four. Under the simplified assumptions, each conception is a separate random event; earlier children do not change the probability for the next conception. Across many offspring, the observed proportion often approaches the model value while remaining subject to chance variation. A particular small family therefore need not show an exact 1:2:1 ratio.

Aa denotes a heterozygous genotype with one A and one a allele. For a fully recessive trait, aa shows the recessive phenotype; in the simple model, Aa is a carrier without that recessive appearance. Thus the recessive genotype and phenotype probabilities for Aa×Aa are each 1/4 when the dominance assumption applies. Real genetic traits may involve several genes, environmental factors or variable expression. This school-level equation explains a Mendelian model and is not an individual medical risk assessment. Genotype names the alleles; phenotype describes the observable trait.