Chapter 18, Problem 1CS

To determine

Whether the provided probabilities satisfy the probability rules.

Answer to Problem 1CS

Solution: The provided probabilities do not satisfy the probability rule B, they only satisfy the probability Rule A.

Explanation of Solution

Calculation:

The probability Rules A and B is stated below:

Rule A states that all the probabilities of the outcomes must be a number between 0 and 1.

Rule B states that the sum of probabilities of all the outcomes must be exactly equal to 1.

The provided probabilities to win the Super Bowl 50 are all between 0 and 1. Hence, Rule A can be accommodated.

To verify Rule B, check whether the sum of probabilities of all the outcomes is exactly equal to 1.

Now, calculate the sum of the probabilities from the referred table 18.1 as shown below:

$\begin{array}{c}\text{Probability}=\left(\begin{array}{l}P\left(\text{Green Bay Packers}\right)+P\left(\text{New England Patriots}\right)+\\ P\left(\text{Seattle Seahawks}\right)+\dots +P\left(\text{Jacksonville Jaguars}\right)\end{array}\right)\\ =\frac{1}{5}+\frac{1}{7}+\frac{1}{11}+\dots +\frac{1}{301}\\ =1.16\end{array}$

Thus, the obtained sum of the probability is 1.16. Hence Rule B cannot be accommodated.