II. (20%) Suppose that you want to develop a program to identify a presidential candidate based on the words they use in their speeches. You have collected a sample of transcripts from each presidential candidate's recent speeches, and candidate A's speeches make up 10% of the sample. Suppose the proportion of A's speeches that have the following five words are given below.

| great | 0.51 |
| --- | --- |
| economy | 0.45 |
| stupid | 0.34 |
| fake | 0.14 |
| rich | 0.14 |

Assume the proportions of other candidates' speeches that have the same words are

| great | 0.015 |
| --- | --- |
| economy | 0.022 |
| stupid | 0.022 |
| fake | 0.041 |
| rich | 0.011 |

(a) If a transcript from the sample includes the word "great", what is the probability that this speech is given by candidate A? Should your program label this transcript as candidate A's speech?