# Likelihood for a test data (sequence of characters) given unigram models

I would like to find the likelihood of a sequence of characters (the test data), given two unigram models.

The sequence (test data) is:

``````A B C B B
``````

The models are:

``````       Model 1       Model 2
P(A)     0.3           0.4
P(B)     0.4           0.5
P(C)     0.3           0.1
``````

Basically, I would like to know the likelihood, and if I can make a prediction as to which model the sequence belong and the underlying assumptions. I understand that given any unigram language model, the likelihood (or probability) of any sequence of characters is p(sequence of characters|Model).

What I have done so far was to find the MLE for each character:

P(A) =1/5 ; P(B) = 2/5 ; P(C) = 1/5

I don't know how to compute p(sequence of characters|Model). Should I multiply these to find the likelihood and establish which model it came from? How to handle the model probabilities given?

Under this assumption, the likelihood of `A B C B B` is just the product of the individual probabilities for each letter.