Mathematics — Standard (041) — CBSE Class 10 board question

When three coins are tossed, the sample space is:
{HHH, HHT, HTH, THH, HTT, THT, TTH, TTT} — Total = 8 outcomes.

(i) At least one head:
Favourable outcomes: HHH, HHT, HTH, THH, HTT, THT, TTH → 7 outcomes

$$P(\text{at least one head}) = \frac{7}{8}$$

(ii) Exactly two tails:
Favourable outcomes: HTT, THT, TTH → 3 outcomes

$$P(\text{exactly two tails}) = \frac{3}{8}$$

(iii) At most one tail:
Favourable outcomes (0 or 1 tail): HHH, HHT, HTH, THH → 4 outcomes

$$P(\text{at most one tail}) = \frac{4}{8} = \frac{1}{2}$$

Source: Chapter 14 — Probability, Section 14.1

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• List the sample space first — examiners look for this; it shows method and avoids errors.
• "At least one" means 1 or more; use complement: $1 - P(\text{no head}) = 1 - \tfrac{1}{8} = \tfrac{7}{8}$ is an equally valid approach.
• "At most one tail" means 0 tails or 1 tail — a common source of confusion; do not include TTH, THT, HTT (those have 2 tails).
• Always simplify fractions where possible (e.g., $\tfrac{4}{8} = \tfrac{1}{2}$).