Three coins are tossed, and the number of heads is recorded. Which of the following lists is a sample space for the experiment?
Why do the other lists fail to qualify as a sample space?
(i) {1, 2, 3} (ii) {0,1, 2} (iii) {0, 1, 2, 3, 4} (iv) {0, 1, 2, 3}

Possible outcomes when tossing 3 coins are :
\(\{HHH, HHT, HTH, THH, HTT,THT,TTH,TTT\}\)
Now count the number of heads in each outcome

Outcome	Number of Heads
HHH	3
HHT	2
HTH	2
THH	2
HTT	1
THT	1
TTH	1
TTT	0

So the possible number of heads are: \(0, 1, 2, 3\)
Hence, the correct sample space is \(\{0, 1, 2, 3\}\)
Therefore, option (iv) is correct.

(i)\(\{1, 2, 3\}\)
This list does not include \(0\).
But getting no heads is possible: \(TTT → 0\,heads\)
So this is not a complete sample space.

(ii)\(\{0, 1, 2\}\)
This list does not include \(3\).
But getting three heads is possible: \(HHH → 3\,heads\)
So this list is also incomplete.

(iii)\(\{0, 1, 2, 3, 4\}\)
This list included \(4\). But when 3 coins are tossed, getting 4 heads is impossible.
A sample space must contain only possible outcomes. So this list is invalid.