PLEASE PROVIDE A DETAILED EXPLANATION. ALSO PROVIDE THE FORMULA.

Directions: Perform an experiment for each event and then list all the possible outcomes. Write your answer on a separate sheet of paper. A. Each of the letters of the word "MATHEMATICS" is written on a separate card. The cards are placed faced down and shuffled. A card is chosen at random. What is the probability that it will show each of the following? 1. The letter M 3. The letter E 2. A vowel 4. The letter T B. There are 3 ways of performing Task A. There are 4 ways of performing Task B. Find the number of ways there are to perform Task A and then Task B. Show this through a tree diagram