When two dice are thrown, the sample space is 

S = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6), (6, 1), (6, 2), (6, 3), (6,4), (6, 5), (6, 6)} 

∴ n(S) = 36 

(a) Let event A: Sum of the numbers on uppermost face is 5. 

∴ A = {(1, 4), (2, 3), (3, 2), (4, 1)} 

∴ n(A) = 4

∴ P(A) = \(\frac {n(A)}{n(S)} = \frac {4}{36} = \frac {1}{9}\)

(b) Let event B: Sum of the numbers on uppermost face is at least 8 (i.e., 8 or more than 8) 

∴ B = {(2, 6), (3, 5), (3, 6), (4, 4), (4, 5), (4, 6), (5, 3), (5, 4), (5, 5), (5, 6), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

∴ n(B) = 15

 ∴ P(B) = \(\frac {n(B)}{n(S)} = \frac {15}{36} = \frac {5}{12}\)

(c) Let event C: First throw gives a multiple of 2 and second throw gives a multiple of 3. 

∴ C = {(2, 3), (2, 6), (4, 3), (4, 6), (6, 3), (6, 6)} 

∴ n(C) = 6

  ∴ P(C) = \(\frac {n(C)}{n(S)} = \frac {6}{36} = \frac {1}{6}\)

(d) Let event D: The product of the numbers on uppermost face is 12. 

∴ D = {(2, 6), (3, 4), (4, 3), (6, 2)} 

∴ n(D) = 4

   ∴ P(C) = \(\frac {n(D)}{n(S)} = \frac {4}{36} = \frac {1}{9}\)