Since either coin can turn up Head (H) or Tail (T), are the possible outcomes.

Let us assume that 1, 2, 3, 4, 5 and 6 are the possible outcomes when the die is thrown.

The problem can be solved by dividing it into 3 cases

Case 1: The outcome is Head and the corresponding number on the die shows Odd number

Total number of sample space = (1 × 3) = 3

Sample space S_{HO }= {(H,1), (H,3), (H,5)}

Case 2: The outcome is Head and the corresponding number on the die shows Even number

Total number of sample space = (1 × 3 × 6) = 18

S_{HE}={(H,2,1),(H,2,2),(H,2,3),(H,2,4),(H,2,5),(H,2,6),(H,4,1),(H,4,2),(H,4,3),(H,2,4),(H, 4,5),(H,4,6), (H,6,1),(H,6,2),(H,6,3),(H,6,4),(H,6,5),(H,6,6)}

Case 3: The outcome is Tail

Total number of sample space=1

Sample space S_{T }= {(T)}

The overall sample spaces

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

(H,4,6), (H,6,1),(H,6,2),(H,6,3),(H,6,4),(H,6,5),(H,6,6),(T)}

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