Question

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

• A. $S=\{H,TH,TTH,HTTH,TTTTH,\cdots \}$
• B. $S=\{H,TH,THH,TTTH,THHTH,\cdots \}$
• C. $S=\{H,TH,TTH,TTTH,TTTTH,\cdots \}$
• D. $S=\{T,TH,TTH,TTTH,TTTTH,\cdots \}$

Answer 1

The correct option is C $S=\{H,TH,TTH,TTTH,TTTTH,\cdots \}$

In the experiment head may come up on first toss, or the $2nd$ toss, or the $3rd$ toss and so on till head is obtained. Hence, the desired sample space is
$S=\{H,TH,TTH,TTTH,TTTTH,\cdots \}$