Chapter 5.1, Problem 11E

(a)

To determine

To explain why these two outcomes have exactly the same probability.

Explanation of Solution

The winning numbers might be for example $2873\text{ or 9999}$ . It is given that both of these two have exactly the same probability. Thus, these two have exactly the same probability because each of these numbers is only one out of $10000$ four digit numbers possible, ranging from $0000\text{ to 9999}$ . Thus we can say that both have exactly the same probability.

(b)

To determine

To find out using the information in this section which of the numbers is the winning number and explain why and also explain how might this affect the four digit number you would choose.

Answer to Problem 11E

The winning number be $2873$ by using the information.

Explanation of Solution

By using the information given in the section, we can say that most people would probably say that $2873$ is the more likely number because they would consider it unlikely for the number $9$ to appear four times in a row. However, it is just as likely for the numbers $2,8,7,\text{ and }4$ to appear in that exact order. Thus, the winning number be $2873$ by using the information.