Question

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

Tossing a fair coin twice.

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 a fair coin twice.

Step 2. Construct probability model.

Considering the following outcomes for each toss:

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

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

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

The probability of each outcome will be

localid="1647515505298" $P\left(HH\right)=\frac{1}{4},P\left(HT\right)=\frac{1}{4},P\left(TH\right)=\frac{1}{4},P\left(TT\right)=\frac{1}{4}$

We got this since of them appeared once in the sample space with 4 total outcomes. If we will add them together, it will equal 1.

Step 3. Conclusion.

The list of possible outcomes:

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

The probability of each outcome:

$P\left(HH\right)=\frac{1}{4},P\left(HT\right)=\frac{1}{4},P\left(TH\right)=\frac{1}{4},P\left(TT\right)=\frac{1}{4}$