Question

In Problems 11–16, construct a probability model for each experiment.

Tossing three fair coins once.

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 three fair coins once.

Step 2. Construct probability model. 

Considering the following outcomes for each toss:

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

The list of possible outcomes in tossing three coins once 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$\frac{1}{8}$.