Given a vocabulary V of |V | = 10, 000 unique words, use the Laplacian smoothing to estimate the probability Pr(dinner|foods) and Pr(foods|dinner) based on the following corpus:

I dont like to have lunch with a lot of foods.

There are a lot of dinner foods today.

The grocery has various foods for dinner.

Make sure you write down the equations for these two probabilities and then substitute the terms with concrete counts based on the corpus to find the ratios.