Q.Three coins are tossed together. Write the sample space, and list the outcomes in the event 'at least two heads appear'.

[!TLDR] List all $2^3=8$ outcomes, then pick those with $2$ or $3$ heads. [!ANSWER] $S={HHH,HHT,HTH,HTT,THH,THT,TTH,T …

Each of the three coins independently shows H or T, giving $2\times2\times2=8$ outcomes in total: $S = \{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT\}$. 'At least two heads' means exactly two heads or exactly three heads. The outcomes with exactly three heads: $HHH$ (one way). The outcomes with exactly two heads (one tail, in any of the three positions): $HHT$, $HTH$, $THH$ (three ways). Combinin …

List the full $8$-outcome sample space systematically (all HHH-type strings), then scan it and pi …

A common mistake is only listing the exactly-two-heads outcomes and forgetting to also include the exactly-three-heads outcome $HHH …