Suppose that an experiment consists of picking at random a bit string of length 5...

Consider the following events...

E1 : the bit string choose begins with 1

E2 : the bit string choose ends with 1

E3 : the bit string choose has exactly three 1' s

(a) Find P(E1), P(E2), P(E3)

(b) Find p(E1/E3)

(c) Find p(E3/E2)

(d) Find p(E2/E3)

(e) Find p(E3/E1E2)

(f) determine whether E1 and E2 are independent

(f) determine whether E2 and E3 are independent