Consider the following sentence: "Engineering is a complex endeavor." Assume that an HMM POS tagger is used to choose between these two tag-sequences (involving Penn Treebank POS tags) for the given sentence: Engineering/NN is/VBZ a/DT complex/NN endeavor/NN./. Engineering/NN is/VBZ a/DT complex/JJ endeavor/NN./. In other words, the system is only considering a single tag for most of the words, but the word "complex" can be tagged as either a singular noun or an adjective. Without stating any actual numbers, show which tag transition probabilities and word observation likelihoods (a.k.a. emission probabilities) will determine the choice for this tag. In terms of these probabilities, express an equation that must hold for the JJ tag to be chosen. Consider the following sentence: "Engineering is a complex endeavor." Assume that an HMM POS tagger is used to choose between these two tag-sequences (involving Penn Treebank POS tags) for the given sentence: Engineering/NN is/VBZ a/DT complex/NN endeavor/NN./. Engineering/NN is/VBZ a/DT complex/JJ endeavor/NN./. In other words, the system is only considering a single tag for most of the words, but the word "complex" can be tagged as either a singular noun or an adjective. Without stating any actual numbers, show which tag transition probabilities and word observation likelihoods (a.k.a. emission probabilities) will determine the choice for this tag. In terms of these probabilities, express an equation that must hold for the JJ tag to be chosen