Final answer:
The most likely explanation is that a mutation occurred in the core promoter of one of the lac operons.
Step-by-step explanation:
The most likely explanation for the observed results is option B: A mutation occurred in the core promoter (-10 or -35 sites) of one of the two lac operons.
The lac operon is a set of genes that encode proteins involved in the metabolism of lactose. In the presence of glucose, the lac operon is usually repressed, meaning that the proteins encoded by the operon are not produced. When glucose is absent and lactose is present, the lac operon should be turned on and the proteins should be produced. However, the observation that only half as much of the proteins are produced suggests that there is a mutation in one of the core promoter sites of one of the operons.
The core promoter is a region of DNA where the RNA polymerase binds to initiate transcription. A mutation in the core promoter can disrupt the binding of RNA polymerase, leading to reduced transcription and protein production. Therefore, option B is the most likely explanation for the observed results.