3. After completing this lesson you will learn:  To find the probability of independent events.  To find the probability of dependent events.

4. Vocab with Review Lesson Check your Skills Mini Quiz

5.  Probability- the probability of an event, or P(event), tells you how likely it is that something will occur.  Outcome- is the result of a single trial, like one roll of a number cube.  Sample Space-is all the possible outcomes.  Event- is any outcome or group of outcomes.

6. Theoretical Probability Experimental Probability  When all possible outcomes are equally likely, you can find theoretical probability of an event using the following formula: P(event) = number of favorable outcomes number of possible outcomes Probability based on data collected from repeated trials is experimental probability, which is shown in the following formula: P(event) = number of times an event occurs number of times the experiment is done Next, click to see example of Theoretical Probability & Experimental Probability Next, click to see example of Theoretical Probability & Experimental Probability

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8.  Next, click here to watch a video over, Theoretical vs. Experimental Probability

10.  Complement of an event: consists of all the outcomes not in the event.  Odds- describes the likelihood of an event by comparing favorable and unfavorable outcomes. Odds in favor of an event  number of favorable outcomes to number of unfavorable outcomes Odds against an event  number of unfavorable outcomes to number of favorable outcomes Next, click to see an example of Finding the Odds

11. Question: Find the odds in favor of the spinner landing on a number greater than or equal to 6. Solution: Odds in favor of an event  number of favorable outcomes to number of unfavorable outcomes  Favorable outcomes: 6,7,8 ◦ (3 numbers)  Unfavorable outcomes: 1,2,3,4,5 ◦ (5 numbers) ANSWER : The odds are 3:5

12. Great job! You have just completed your 2.6 Vocab & Review! start on Lesson 2.7 Please click the button below to go back to the main menu and start on Lesson 2.7. MAIN MENU

13. Probability of Compound Events Before we get into the “nitty gritty” of Probability of Compound Events you should have already reviewed information from the previous lesson. So let’s check your skills and do a few questions. Please note, the questions asked are skills needed in order to ‘move on’ and truly understand Probability of Compound Events. Please click on the button below to continue: CHECK YOUR SKILLS

14. For questions #1-2, please Find the probability for one roll of a number cube. 1. P(multiples of 3) a. ½ b. 1/6 c. 1/3 d. 5/6

15. Yes, 1/3 is the probability of rolling a multiple of 3. Click to go to #2

16. PLEASE TRY AGAIN! If a cube has numbers 1-6…Think, “what are the multiples of 3 on that dice?” TRY AGAIN!

17. Reminder, find the probability for one roll of a number cube. 2. P(greater than 4) a. 1/6 b. 2/3 c. 1/3 d. 5/6

18. Yes, 1/3 is the probability of rolling a number greater than 4. You are now done reviewing…click below to start learning Lesson 2.7 Begin 2.7

19. PLEASE TRY AGAIN! If a cube has numbers 1-6, how many are greater than 4? TRY AGAIN!

20. NEW VOCABULARY:  Independent events- are events that do not influence one another.  Dependent events- are events that do influence each other. The occurrence of one event affects the probability of a second event.

21. Rule: Probability of Two Independent Events  If A & B are independent events,  P(A and B)=P(A)*P(B).

22. Rule: Probability of Two Dependent Events  If A & B are dependent events,  P(A then B)= P(A)*P(B after A). Next, click here to watch a video on Independent Events & Dependent Events Next, click here to watch a video on Independent Events & Dependent Events

24. Suppose you roll a red number cube and a blue number cube. What is the probability that you will roll a 3 on a red cube and even number on a blue cube? Solution: P(red 3) = (There is only one way to get a 3 out of six numbers) P(blue even) = = (There are three even numbers out of six numbers) P(red 3 and blue even) = P(red 3) * P(blue even) = * = ANSWER: The probability that you will roll a 3 on the red number cube and even number on the blue cube is

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26. I, U, I, A, O, O, O, E, A, U, A, O, A, E, E. Suppose you choose a tile at random from the same letters in example 2: I, U, I, A, O, O, O, E, A, U, A, O, A, E, E. Without replacing the tile, you select a second tile. What is the probability that you will choose an A and then an E? ◦ P(A) = ◦ P(E after A)= ◦ P(A then E) = P(A) *P(E after A) = ANSWER: The probability that you will choose an A and then an E is

27. Nice job! You are now done going over Lesson 2.7…if you feel like you need to go back and look through the examples again or take better notes, feel free to head to the main menu and click on Lesson 2.7 again or 2.6 if you feel necessary. If not, you may begin your mini quiz over the two sections. Good Luck! MAIN MENU Mini Quiz

28. 1. You take a three-question true false quiz. You guess on all the questions. What is the probability that you will get a perfect score? a. b. c. d.

29. You have a bag containing 3 green marbles, 4 red marbles, and 2 yellow marbles. You select 1 marble randomly. What are the odds against selecting green or yellow marble? a. 5:4b. 9:4 c. 4:9d. 4:5

30. Suppose you select a two-digit number at random from 10 to 30 (including 10 and 30). Find P(number is a multiple of 6): a. 11:21 b. 4:21 c. 1:5 d. 1:7

31.  Click to go on

32. PLEASE TRY AGAIN! You may want to be looking at your notes. Hint: Look at your formula for Independent Events. TRY AGAIN!

33.  Click to go on

34. PLEASE TRY AGAIN! Make sure you make note that this question is an example of “selecting without replacement.” TRY AGAIN!

35. Yes, the odds against are 4:5 of the event. Go to last question

36. PLEASE TRY AGAIN! Remember… Odds against an event  number of unfavorable outcomes to number of favorable outcomes. TRY AGAIN!

37. GREAT JOB!!! Yes, 4:21 is the probability of selecting a number that is a multiple of 6…(12,18,24,30…4 numbers, out of a total of 21 possible numbers). NEXT?

38. PLEASE TRY AGAIN! Remember, the numbers can include 10 and 30. It may help to make a list that way you have a visual. TRY AGAIN!

39. You are all done with your StAIR!!! I hope you took good notes and have mastered your learning of probability. If for any reason, you want to go back and look at things, feel free to head back to the main menu. MAIN MENU