Final answer:
The probability that the F2 offspring will have the phenotype A1B1C1 in a trihybrid cross is calculated using the product rule and the given ratios, resulting in a value of 3/64.
Step-by-step explanation:
The question pertains to a trihybrid cross where offspring phenotypes for three separate genes (A, B, and C) are considered. For F2 offspring, the phenotypes received from each gene can be determined based on the independent assortment of alleles and their corresponding probabilities. The given ratios for A1:A2, B1:B2, and C1:C2 are 1/4:3/4, 1/4:3/4, and 3/4:1/4 respectively. To calculate the probability that the F2 offspring will have the phenotype A1B1C1—a combination of the first listed trait from each of the three genes—we need to multiply the probabilities of each individual trait being expressed. Using the product rule for independent events, the combined probability is (1/4) for A1 times (1/4) for B1 times (3/4) for C1.
Therefore, the probability is:
(1/4) × (1/4) × (3/4) = 3/64.
The probability that F2 offspring will have the phenotype A1B1C1 in a trihybrid cross with independent assortment is 3/64.