Question

A coin is flipped until 3 heads in succession occur. List only these elemnt of the sample space that require 6 or less tosses is this a discrete sample space explain?

Answer 1

Let $H$ be the head and $T$ be the tail. A coin is flipped until 3 heads in succession occur.

The sample space of the experiment is

$S=\{HHH,THHH, HTHHH,TTHHH, HTTHHH,$

$TTTHHH, HTTTHHH,...\}$

List of elements of the sample space that requires 6 or less tosses is

$L=\{HHH, THHH, TTHHH, TTTHHH,$

$HTHHH, HTTHHH, HHTHHH, THTHHH \}$

The sample set is discrete as the space contains a finite number of possibilities with as many elements as there are whole numbers.