Final answer:
To calculate the probability of an offspring with the genotype AABBCC from a cross between two AaBbCc organisms, we use the product rule across all three independently assorting genes, resulting in a combined probability of 1/64, or 1.56%.
Step-by-step explanation:
The question involves calculating the probability of producing an offspring with a specific genotype (AABBCC) when two organisms with the genotype AaBbCc are crossed. To determine this, we apply Mendel's laws of inheritance, particularly the law of independent assortment and the use of Punnett squares or the forked-line method. Each gene pair segregates independently, so we must determine the probability for each gene and then combine them.
For gene A: Cross Aa x Aa. The likelihood of producing an AA offspring is 1/4, as the possible combinations are AA, Aa, aA, and aa, based on Mendelian genetics.
For gene B: Similar to gene A, Bb x Bb also has a 1/4 chance of resulting in BB offspring.
For gene C: Again, Cc x Cc results in a 1/4 chance of producing CC offspring.
Using the product rule to find the combined probability of independent events, we multiply the individual probabilities: (1/4 for A) x (1/4 for B) x (1/4 for C) = 1/64.
Therefore, the probability of producing an offspring with the genotype AABBCC is 1/64, or about 1.56%.