1. Independent Events

2. These situations are dealing with Compound events involving two or more separate events. These situations are dealing with Compound events involving two or more separate events. When will the occurrence of one event effect the occurrence of another? When will the occurrence of one event effect the occurrence of another?

3. Lets Play MONOPOLY GO TO JAIL! GO TO JAIL! To get out of Jail you must roll doubles on a pair of standard diceTo get out of Jail you must roll doubles on a pair of standard dice

4. Lets look at the following Questions 1. Determine the probability that you will roll doubles on your first try.

5. Let A represent the event that a double is rolled You could get a double 1, 2,3,4,5 or 6 … This gives you 6 possible outcomes When you roll a dice there are 36 different outcomes

6. 2. On your first two turns you failed to roll doubles. One of your opponents’ reasons that on the next turn your odds of rolling doubles is 50/50. Explain how your opponents’ reasoned this.

7. -A be the even that you roll a double on your first try. -B be the event that you roll a double on you second try -C be the event that you roll a double on your third try. After two unsuccessful trials, the probability has risen to 3/6 or even odds.

8. 3. What is the probability that you will get out of jail on the third attempt?

10. 4. After how many turns is it certain that you will roll doubles? Explains.

11. Infinite. There is no trial in which the probability is equal to one.

12. 5. One of your opponents, explain that each roll of the dice is an independent event and that, since the relatively low probability of rolling doubles never changes from trial to trial, you may never get out of jail and may as well forfeit the game. Explain the flaw in this analysis. What is correct in this analysis?

13. While the probability of rolling doubles on any one trial is relatively low, 1/6. There is still a non-zero probability of the event occurring. In fact, over a large number of trials, we would expect to see doubles rolled once out of every six trials. Thus, you have a significant likelihood of getting out of jail before the game is over.

14. Summary Note In some situations involving compound events, the occurrence of one event has no effect on the occurrence of another These events are INDEPENDENT

15. Ex a) A coin flipped and turns up heads. What is the Probability that the second flip will turn up heads? a) A coin is flipped four times and turns up heads each time What is the probability that the fifth will turn up heads?

16. c) What is the probability of tossing five heads in a row? The Compound Probability of two independent events can be calculated by using the Product Rule for Independent Events

17. Examples 1. A coin is flipped and a spinner with three equal sections (Red, blue and yellow) is spun. What is the probability of a head and yellow? 2. A calculator has a keyboard assembly and a logic circuit. The probability of a defective keyboard is 0.05 and the probability of a defective circuit is 0.02. What is the probability that a calculator will not be defective when it is assembled?

18. Homework! Pg 334 #1,2,3,4ab