Sample space = S = {HHH,HHT,HTH,HTT,THH,THT,TTH,TTT},

The sample space S has 8 elements, i.e., n(S) = 8

where the first letter represents how the nickel came up,
the second letter represents how the dime came up, and
the third letter represents how the quarter came up.

E = {HHH,HHT,HTH,THH}. There are 4 elements so n(E) = 4

F = {HHH,HTH,THH,TTH}. There are 4 elements so n(F) = 4

1. n(E ∩ F) = n({HHH,HHT,HTH,THH} ∩ {HHH,HTH,THH,TTH}) = n({HHH,HTH,THH})
[Note: ∩ means to take ONLY the elements in common.]

There are 3 elements so n(E ∩ F) = 3

2. P(E) = n(E)/n(S) = 4/8 = 1/2 

3. P(F) = n(F)/n(S) = 4/8 = 1/2 

4. P(E ∩ F) = n(E ∩ F)/n(S) = 3/8

Edwin