In an experiment, you pick at random a bit string of length 5. Consider the following events: E1: the bit string chosen begins with 1, E2: the bit string chosen ends with 1, E3: the bit string chosen has exactly three 1s.
(a) Find P(E1 ∩ E3).
(b) Find P(E3 ∩ E2).
(c) Find P(E2 | E3).
(d) Find P(E1 ∩ E2 ∩ E3).
(e) Determine whether E1 and E2 are independent.
(f) Determine whether E2 and E3 are independent.