List (iv) {0, 1, 2, 3} is the correct sample space because three tossed coins can yield 0, 1, 2 or 3 heads. The other lists either omit possible outcomes or include an impossible outcome.
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? (i) {1, 2, 3} (ii) {0, 1, 2} (iii) {0, 1, 2, 3, 4} (iv) {0, 1, 2, 3}
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The correct sample space is (iv) {0, 1, 2, 3}.
When tossing three coins, the number of heads can be 0 (TTT), 1 (HTT, THT, TTH), 2 (HHT, HTH, THH) or 3 (HHH).
Why the others fail:
(i) {1, 2, 3} fails because it misses 0 heads.
(ii) {0, 1, 2} fails because it misses 3 heads.
(iii) {0, 1, 2, 3, 4} fails because getting 4 heads from 3 coins is impossible.
For more NCERT Solutions of Class 9 Ganita Manjari Chapter 7 The Mathematics of Maybe: Introduction to Probability Question Answer (2026-27)
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