Mutually Exclusive or Not

 I was thinking about mutually exclusive and independent events and one of the easy example one can conjure up is with two coins.
Experiment: Tossing two coins

Mutually Exclusive

E1: Head on both coins => 1/4
E2: Tails on both coins => 1/4
E3: E1 or E2
P(E3) = P(E1)+P(E2) => 1/4+1/4 = 1/2

Not Mutually Exclusive
E4: Head on one coin => 3/4
E5: Tail on one coin => 3/4
E6: E4 or E5
P(E6) = P(E4)+P(E5) = 3/4+3/4 = 3/2 which is ><
The reason is the above two are not mutually exclusive as both E4 and E5 could happen when we have a {HT, TH}