Final answer:
Most likely, Texas would still be part of Mexico today if it had not won its independence, as the other scenarios are less plausible given the historical context.
Step-by-step explanation:
If Texas had not won their independence, the most likely scenario is that it would still be part of Mexico today. Given the history and the eventual victory of Texas against a weaker Mexican government during the Texas Revolution, the options of becoming a British colony or being an independent nation after failing to attain independence seem less plausible.
Prior to the events leading to the independence of Texas, the southwestern United States was all part of Mexico. The victory of Texas and the establishment of the Lone Star Republic, backed by figures like Sam Houston, followed by the eventual annexation to the United States, suggest that without this path to independence, Texas would not have been in a position to become an American state or an independent nation.