In a trihybrid cross, the probability of showing at least one dominant trait is
Trihybrid cross AaBbCc x AaBbCc with independent assortment and complete dominance at each locus involves three independent segregation events. Probability offspring receives no dominant allele, i.e., homozygous recessive aabbcc, equals product of individual recessive probabilities (1/4)*(1/4)*(1/4)=1/64. Complementary event showing at least one dominant trait therefore equals 1 minus all recessive probability, 1-1/64=63/64. Calculation employs product rule for independent events and complement rule for union. Includes classes expressing one, two, or three dominant phenotypes, useful for predicting proportions in multigenic traits.
Ref: Griffiths et al., Introduction to Genetic Analysis, 12th ed., Chapter 2: Probability Rules for Trihybrid Cross