Please clearly explain how you get answers (including what theorem you use, etc) for each part.

Suppose that four letters are selected from the collection {13, F, G, H, I, J} at random with replacement, and Written in order to form a \"word\". a) Let 3 denote the sample space consisting of all outcomes of this experiment. Compute the number of outcomes in S. b Let A be the event that the word begins and ends with a vowel. Compute P(.A). G Let B be the event that the word contains all distinct letters. Compute P(B) (1 Compute P(.A D B) and P(.A U B). e Are A and 5 independent events? Justify your answer. ) ) ) )