An experiment consists of rolling a die and then tossing a coin once if the number on the die is even. If the number on the die is odd, the coin is tossed twice. Write the sample space for this experiment.

The sample space obtained by rolling a die is

S_{1} = {1,2,3,4,5,6}

If the number on the die is even i.e., 2, 4 or 6, we toss a coin with sample space

S_{2} = {H, T}

If the number is odd i.e, 1, 3 or 5, we toss two coins with sample space

S_{3} = {HH, HT, TH, TT}

Hence, the combined sample space is :

S = {2H, 2T, 4H, 4T, 6H, 6T, 1HH, 1HT, 1TH, ITT, 3HH, 3HT, 3TH, 3TT, 5HH 5HT, 5TH, 5TT}