1. [25 marks] Imagine that you would like to predict if your favorite table will be free at your favorite restaurant. The only additional piece of information you can collect, however, is if it is sunny or not sunny. Therefore, you would like to predict whether the table will be free or not given the weather. You collect paired samples from visit of the form (is sunny, is table free), where it is either sunny (1) or not sunny (0) and the table is either free (1) or not free (0). Your goal is to learn P(Table is Free|Weather Information), which then also automatically tells you P(Table is Not Free|Weather Information) by taking 1-P(Table is Free|Weather Information). Given these learned probabilities, you can make predictions about whether your table is free or not by checking if P(Table is Free|Weather Information) > 0.5. If there is a greater than 50% probability your table is free, you are happy to risk the icy streets to get to your favorite restaurant. Hint: To help you with this question, see Section 5.4, Example 24 about books