Chapter 7.3, Problem 7.55E

To determine

To Explain: that two events are independent.

Explanation of Solution

Calculation:

Suppose that A be the event of rolling a red die and B the event of rolling a green die. There the two events are independent, because the two dice are independent and therefore the corresponding events would be independent.

For example rolling a red die, then 1 chance in 5 to roll a 5 with the green die (which does not depend on the red)

  $\text{P}\left(\text{5}\text{on}\text{green die | 5 on red die}\right)=\frac{1}{6}$

Generally, there will be 1 chance in 5 to roll a fair die.

  $\text{P}\left(\text{5 on green die}\right)=\frac{1}{6}$

Since $\text{P}\left(\text{5}\text{on}\text{green die | 5 on red die}\right)=\text{P}\left(\text{5 on green die}\right)$ , so two events are independent.