Question

In Problems 11–16, construct a probability model for each experiment.
Tossing one fair coin three times.

Short answer

The list of possible outcomes: $S=\left\{\mathrm{HHH},\mathrm{HHT},\mathrm{HTH},\mathrm{HTT},\mathrm{THH},\mathrm{THT},\mathrm{TTH},\mathrm{TTT}\right\}$

The probability of each outcome will be$\frac{1}{8}$.

Step-by-step solution

Step 1. Given information.

Construct a probability model for experiment: Tossing one fair coin three times.

Step 2. Construct probability model.  

Considering the following outcomes for each toss:

First toss - A head (H) or a tail (T), Second toss - A head (H) or A tail (T), Third toss - A head (H) or a tail (T) .

The list of possible outcomes in tossing a fair coin thrice will be:

$S=\left\{\mathrm{HHH},\mathrm{HHT},\mathrm{HTH},\mathrm{HTT},\mathrm{THH},\mathrm{THT},\mathrm{TTH},\mathrm{TTT}\right\}$

The probability of each outcome will be $\frac{1}{8}$since each of them appeared once in the sample space with 8 total outcomes. If we will add them together, it will be equal to 1.

Step 3. Conclusion.  

The list of possible outcomes: $S=\left\{\mathrm{HHH},\mathrm{HHT},\mathrm{HTH},\mathrm{HTT},\mathrm{THH},\mathrm{THT},\mathrm{TTH},\mathrm{TTT}\right\}$

The probability of each outcome will be$\frac{1}{8}$.