A coin is tossed. If the result is a head, a die is thrown. If the die shows up an even number, the die is thrown again. What is the sample space for this experiment.

Explanation

When a coin is tossed then
S1={H,T}

When the coin shows T, then there is no action. When the coin shows H, a die is thrown then

S2={1,2,3,4,5,6}

When the die shows {1,3,5}, then there is no action.

When the die shows {2,4,6,} a die is thrown again.

Thus S={T,H1,H3,H5,H21,H22,H23,H24,H25,H26,H41,H42,H43,H44,H45,H46,H61,H62,H63,H64,H65,H66}