Question

Consider the experiment in which a coin is tossed repeatedly until a head comes up. Describe the sample space.

Answer 1

Given:
A coin is tossed repeatedly until a head comes up.

If a coin is tossed and outcome is head then the experiment is over. And, if the outcome is tail, then the coin is tossed again. In the second toss also if the outcome is head, then experiment is over, otherwise coin is tossed again. This process continues infinitely many times until it shows up heads.

Hence, the sample space is $S=\{H,TH,TTH,TTTH,TTTTH,\dots \}$