4.) Express your answers as simply as possible. In a certain experiment, a 5-letter

word is formed by randomly arranging all the letters of the word POPPY. Let E be the event

that the word begins with the letter P, and F be the event that all 3 Ps are grouped together

in the word (i.e. the word has 3 Ps in a row).

(a) Find Pr[E] and Pr[F].

(b) Are E and F independent events?

(c) Find Pr[E|F] and Pr[F|E].