Question

# If a coin is tossed three times (or three coins are tossed together), then describe the sample space for this experiment.

If a single coin is tossed, number of outcomes will be $= 2$
Sample Space $S = \left\{ {H,T} \right\}$
If the coin is tossed three times, no. of outcomes will be ${2^3} = 8$
Sample Space will be the cartesian product of the Set $S$ with itself twice:
$S' = \left\{ {H,T} \right\} \times \left\{ {H,T} \right\} \times \left\{ {H,T} \right\} \\ \Rightarrow S' = \left\{ {HHH,HHT,HTH,HTT,THH,THT,TTH,TTT} \right\} \\$
Note: The number of outcomes in tossing $n$ number of coins $= {2^n}$ . Always remember to check that each outcome in sample space is equally likely to occur. Also, the order of the heads or tails matter in writing sample space of coin tossing experiment.