Answer to Question #298075 in Statistics and Probability for lliana

Question

An experiment consists of asking three Grade 10 students at random if they prefer to choose the Academic track or TVL track in the senior high school. Use A for Academic and T for TVL. Let Y represent the random variable representing the number of TVL track responses.

Answer 1

Let's denote A - Academic, T - TVL.

Sample space S is all possible outcomes of asking.

$$S = \{AAA, TAA, ATA, AAT,$$

$$TTA, TAT, ATT, TTT\}$$

Let $Y$ be a random variable giving the number of heads plus the number of tails in three tosses of a coin. The possible values of $T$ are $0,1,2,3.$

$$\def\arraystretch{1.5} \begin{array}{c:c} Sample\ point & Y \\ \hline AAA & 0 \\ \hdashline TAA & 1 \\ \hdashline ATA & 1 \\ \hdashline AAT & 1 \\ \hdashline TTA & 2 \\ \hdashline TAT & 2 \\ \hdashline ATT & 2 \\ \hdashline TTT & 3 \\ \hdashline \end{array}$$

$$\def\arraystretch{1.5} \begin{array}{c:c} y & 0 & 1 &2 & 3 \\ \hline p(y) & 1/8 & 3/8 & 3/8 & 1/8 \\ \end{array}$$