In a bigram language model, which expression represents the probability of the word 'dog' given the previous word 'the'?

In a bigram language model, which expression represents the probability of the word 'dog' given the previous word 'the'?

• A. p(the | dog)
• B. p(dog | the)
• C. p(dog, the)
• D. p(the, dog)

Answer: (B)

In a bigram language model, the probability of a word depends on the immediately preceding word. To find the likelihood that the next word after “the” is “dog,” you use the conditional probability p(dog | the). This is exactly what the bigram formula captures: P(w_i = dog | w_{i-1} = the). The other forms don’t match that idea. p(the | dog) would be the chance of seeing “the” after “dog,” which is the reverse conditioning. p(dog, the) and p(the, dog) are joint probabilities of the two-word sequence, not the probability of the second word given the first.

In a bigram language model, the probability of a word depends on the immediately preceding word. To find the likelihood that the next word after “the” is “dog,” you use the conditional probability p(dog | the). This is exactly what the bigram formula captures: P(w_i = dog | w_{i-1} = the). The other forms don’t match that idea. p(the | dog) would be the chance of seeing “the” after “dog,” which is the reverse conditioning. p(dog, the) and p(the, dog) are joint probabilities of the two-word sequence, not the probability of the second word given the first.