Question

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

Tossing two fair coins once.

Short answer

The list of possible outcomes: $S=\left\{HH,HT,TH,TT\right\}$.

The probability of each outcome:$P\left(HH\right)=\frac{1}{4},P\left(HT\right)=\frac{1}{4},P\left(TH\right)=\frac{1}{4},P\left(TT\right)=\frac{1}{4}$

Step-by-step solution

Step 1. Given information.

Construct a probability model for experiment: Tossing two 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) .

The list of possible outcomes in tossing two coins once will be:

$S=\left\{HH,HT,TH,TT\right\}$

The probability of each outcome will be:$P\left(HH\right)=\frac{1}{4},P\left(HT\right)=\frac{1}{4},P\left(TH\right)=\frac{1}{4},P\left(TT\right)=\frac{1}{4}$

Step 3. Conclusion. 

The list of possible outcomes: $S=\left\{HH,HT,TH,TT\right\}$.

The probability of each outcome:$P\left(HH\right)=\frac{1}{4},P\left(HT\right)=\frac{1}{4},P\left(TH\right)=\frac{1}{4},P\left(TT\right)=\frac{1}{4}$.