A fair coin is tossed twice. Consider the sample space S = {HH, HT, TH, TT} of equally likely simple events. We are interested in the following events:

E₁ = a head on the first toss

E₂ = a tail on the first toss

E₃ = a tail on the second toss

E₄ = a head on the second toss

For each pair of events, discuss whether they are independent and whether they are mutually exclusive.

(A) E₁ and E₄ 

(B) E₁ and E₂