Question1. What is the difference between independent and dependent events?
2. List examples of the following types of events. (a) Two events that are independent (b) Two events that are dependent
True or False? In Exercises 3 and 4 , determine whether the statement is true 0 false. If it is false, rewrite it as a true statement.
3. If two events are not independent, $P(A \mid B)=P(B)$.
4. If events $A$ and $B$ are dependent, then $P(A$ and $\left.B)=P(A) \cdot P^{\prime} B\right)$.
Classifying Events In Exercises 5-8, decide whether the events are independent or dependent. Explain your reasoning.
5. Selecting a king from a standard deck, replacing it, and then selecting a queen from the deck
6. Rerurning a rented movie after the due date and receiving a late fee
7. Rolling a six-sided die and then rolling the die a second time so that the sum of the two rolls is seven
8. A numbered ball between 1 and 52 is selected from a bin, replaced, and then a second numbered ball is selected from the bin. Classifying Events Based on Studies In Exerciser 9-12, identify the two evenis described in the study. Do the results indicate that the events are independent or dependent? Explain your reasoning.
9. Researchers found that people with depression are five times more likely to have a breathing-related sleep disorder than people who are not depressed.
10. Stress causes the body to produce higher amounts of acid, which can irritate already existing ulcers. But, stress does not cause stomach ulcers. (Source: Aaplor College of Wredicine)
11. Studies found that Aspartame, an artificial sweetener, does not cause memory loss. (Source forad and Drug Adominismation)
12. Acoording to researchers, diabetes is rare in societies in which obesity is rare. In societies in which obesity has been common for at least 20 years, diabetes is also common. (Sowree Ameriom Diaberes Astocianion)