Question

Let T be a random variable giving the number of heads plus the number of tails in three tosses of a coin. List the elements of the sample space for the three tosses of the coin and assign a value to each sample point.

Answer 1

Let's denote H - heads, T - tails.

Sample space S is all possible outcomes of three tosses of a coin.

$$S = \{HHH, THH, HTH, HHT,$$

$$TTH, THT, HTT, TTT\}$$

Let $t$ be a random variable giving the number of heads plus the number of tails in three tosses of a coin. The possible value of $t$ is $3.$

$$\def\arraystretch{1.5} \begin{array}{c:c} Sample\ point & t \\ \hline HHH & 3 \\ \hdashline THH & 3 \\ \hdashline HTH & 3 \\ \hdashline HHT & 3 \\ \hdashline TTH & 3 \\ \hdashline THT & 3 \\ \hdashline HTT & 3 \\ \hdashline TTT & 3 \\ \hdashline \end{array}$$