Three coins are tossed, and the number of heads is recorded. Which of the following lists is a sample space for this experiment? Why do the other lists fail to qualify as a sample space?

(A) {1, 2, 3}
(B) {0, 1, 2}
(C) {0, 1, 2, 3, 4}
(D) {0, 1, 2, 3}

When 3 coins are tossed, the number of heads can be 0, 1, 2, or 3.

(A) $\{1, 2, 3\}$ is invalid.

It misses 0 (the case TTT with zero heads).

(B) $\{0, 1, 2\}$ is invalid.

It misses 3 (the case HHH with three heads).

(C) $\{0, 1, 2, 3, 4\}$ is invalid.

It includes 4, which is impossible (you can't get 4 heads from only 3 coins).

(D) $\{0, 1, 2, 3\}$ is the correct sample space.

It contains exactly these four possible outcomes.