Question

Rolling a die The following figure displays several possible probability models for rolling a die. We can learn which model is actually accurate for a particular die only by rolling the die many times. However, some of the models are not legitimate. That is, they do not obey the rules. Which are legitimate and which are not? In the case of the illegitimate models, explain what is wrong.

Short answer

Model $2$ is the only one that is legal.

Step-by-step solution

Step 1. Given Information  

Using the illustration, which shows multiple different probabilistic models for rolling a die. We must distinguish between valid and illegitimate models, as well as explain why illegitimate models exist.

Step 2. Concept Used   

An event is a subset of an experiment's total number of outcomes. The ratio of the number of elements in an event to the number of total outcomes is the probability of that occurrence.

Step 3. Calculation  

The conditions of the probability distribution are: 1)The probabilities should be $0\le p\le 1$2)

All probability should add up to one. Because all of the probabilities are between $0$and $1$, the model $1,2,3$satisfies the first criteria.

As a result, the Model $4$is not legal. Now we'll look at the model $1,2,3$second condition.

localid="1649652688065" $Model1=\frac{1}{7}+\frac{1}{7}+\frac{1}{7}+\frac{1}{7}+\frac{1}{7}+\frac{1}{7}=\frac{6}{7}$Not satisfied. $Model2=\frac{1}{3}+\frac{1}{6}+\frac{1}{6}+0+\frac{1}{6}+\frac{1}{6}=1$Satisfied.$Model3=\frac{1}{3}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}+\frac{1}{6}=\frac{7}{6}$Not satisfied.