2. PROBABILITY RULES

3. CHANCE IS ALL AROUND YOU….
YOU AND YOUR FRIEND PLAY ROCK-PAPER-SCISSORS TO DETERMINE WHO GETS THE LAST SLICE OF PIZZA….
A COIN TOSS DECIDES WHICH TEAM GETS TO RECEIVE THE BALL FIRST IN THE BEARS GAME….
ADULTS REGULARLY PLAY THE LOTTO IN HOPES OF WINNING A BIG JACKPOT….
OTHERS HEAD TO CASINOS AND RACETRACKS HOPING THAT SOME COMBINATION OF LUCK AND SKILL WILL PAY OFF…
PEOPLE YOUNG AND OLD PLAY GAMES OF CHANCE INVOLVING CARDS OR DICE OR SPINNERS
THE TRAITS THAT CHILDREN INHERIT – GENDER, EYE COLOR, HAIR COLOR, DIMPLES, CLEFTS – ARE DETERMINED BY THE CHANCE INVOLVED IN WHICH GENES GET PASSED ALONG BY THEIR PARENTS

4. A ROLL OF A DICE… A SIMPLE RANDOM SAMPLE… AND EVEN THE INHERITANCE OF YOUR GOOD LOOKS REPRESENT CHANCE BEHAVIOR THAT WE CAN UNDERSTAND AND WORK WITH…..

5. WE CAN ROLL THE DICE AGAIN AND AGAIN AND AGAIN…..

6. THE OUTCOMES ARE GOVERNED BY CHANCE…

7. BUT IN MANY REPITITIONS A PATTERN EMERGES….

8. WE USE MATHEMATICS TO UNDERSTAND THE REGULAR PATTERNS OF CHANCE BEHAVIOR WHEN WE CAN REPEAT THE SAME CHANCE PHENOMENON AGAIN AND AGAIN

9. THE MATHEMATICS OF CHANCE IS CALLED PROBABILITY

10. AND WE WILL SPEND THESE LAST 5 WEEKS OF STATS STUDYING PROBABILITY

11. WELCOME TO PROBABILITY!

12. IN FOOTBALL A COIN TOSS HELPS DETERMINE WHICH TEAM GETS THE BALL FIRST
IN FOOTBALL A COIN TOSS HELPS DETERMINE WHICH TEAM GETS THE BALL FIRST WHY DO THE RULES OF FOOTBALL REQUIRE A COIN TOSS?

13. TOSSING A COIN AVOIDS FAVORTISM

14. FAVORTISM IS UNDESIRABLE

15. THAT’S WHY STATISTICIANS RECOMMEND RANDOMIZED EXPERIMENTS

16. THEY AVOID FAVORTISM BY LETTING CHANCE DECIDE WHO GETS CHOSEN…

17. A BIG FACT EMERGES WHEN WE WATCH COIN TOSSES OR THE RESULTS OF RANDOM EXPERIMENTS CLOSELY

18. CHANCE BEHAVIOR IS UNPREDICATABLE IN THE SHORT RUN, BUT HAS A REGULAR PATTERN IN THE LONG RUN.

19. WHEN YOU FLIP A COIN IT IS EQUALLY LIKELY TO LAND “HEADS” OR “TAILS”

20. DO THUMBTACKS BEHAVE IN THE SAME WAY?

21. IN THIS ACTIVITY YOU WILL TOSS A THUMBTACK SEVERAL TIMES AND OBSERVE WHETHER IT COMES TO REST POINT UP (u) OR POINT DOWN(d)

22. THE QUESTION YOU ARE TRYING TO ANSWER IS… “WHAT IS THE PROBABILITY THAT THE TOSSED THUMBTACK WILL LAND POINT down?”

23. MAKE A GUESS... WHAT PERCENTAGE OF THE TIME DO YOU THINK A THUMBTACK WILL LAND POINT down?

24. WHEN TOSSED ONTO A FLAT SURFACE A COMMON THUMBTACK CAN “POINT UP” OR “Point down”. We are curious, if like a fair coin, these two outcomes are equally likely and if not, what is the probability of each outcome?

25. According to the law of large numbers the long-run relative frequency of repeated independent events gets closer and closer to the true relative frequency

26. Even though the law of large numbers seems natural it is often misunderstood because the idea of long run is hard to grasp! Many people believe that an outcome of a random event that hasn’t occurred in many trials is “due” to occur…. Turn to your partner and give them an example of THE NONexistent law of averages now!

27. a good hitter in baseball player strikes out 6 times in a row so he is “due” for a hit next time up, right?? a girl will be sure to be born next since there are 5 boys in a family, right?? the ball will land on red on the roulette wheel since it has landed on black the last 11 times, right?? you just flipped 5 heads in a row…the coin “OWES” you a tail, right?? right????????????

28. wrong

29. The law of large numbers says nothing about short run behavior.

30. Relative frequencies even out only in the long run
Relative frequencies even out only in the long run! ( and, according to the lln, the long run is really long – infinitely long in fact!)

31. This so called law of averages doesn’t exist at all.

32. Please Open your packet up to page 1

33. A random phenomenon is considered to be any act which______________________________. For example, rolling a die is considered a random phenomenon Turn to your partner and Give another example    

34. A random phenomenon is considered to be any act which can have a random result. For example, rolling a die is considered a random phenomenon Turn to your partner and Give another example    

35. A trial is a _________ attempt of a random phenomenon
  A trial is a _________ attempt of a random phenomenon Rolling a die once for example is one trial of a random phenomenon.  

36. A trial is a single attempt of a random phenomenon
  A trial is a single attempt of a random phenomenon Rolling a die once for example is one trial of a random phenomenon.  

37.   An outcome is ______________________ from any trial of a random phenomenon For example, if the random phenomenon is rolling a die, then rolling it once is a _______and there are ______ different outcomes for this random phenomenon. Another example is rolling a die and flipping a coin. This could result in _________different outcomes.  

38. An outcome is a possible result from any trial of a random phenomenon
  An outcome is a possible result from any trial of a random phenomenon For example, if the random phenomenon is rolling a die, then rolling it once is a trial and there are six different outcomes for this random phenomenon. Another example is rolling a die and flipping a coin. This could result in twelve different outcomes.  

39.   The sample space is ______________________________ of random phenomenon. The sample space for rolling a die is the six outcomes ____________________________________________.  

40.   The sample space is the set of all possible outcomes of random phenomenon. The sample space for rolling a die is the six outcomes 1, 2, 3, 4, 5, 6.  

41. An event is__________________________________
  An event is__________________________________. Technically, an event is any subset of the sample space. For our purposes, we will usually treat event and outcome as the same.  

42. An event is any outcome or set of outcomes
  An event is any outcome or set of outcomes. Technically, an event is any subset of the sample space. For our purposes, we will usually treat event and outcome as the same.  

43. The equally likely condition says ________________________________________ _________________________________________. Give some examples to your partner…

44. The equally likely condition says the outcomes being counted are all equally likely to occur. Give some examples to your partner…

45. According to the law of large numbers the long-run relative frequency of repeated independent events gets closer and closer to the true relative frequency

46. Many people believe that an outcome of a random event that hasn’t occurred in many trials is “due” to occur…. This is referred to as THE law of averages IT IS NOT TRUE!!!

47. The Fundamental counting principle part 1 OR if event A has “m” outcomes and event b has “n” different outcomes then the number of outcomes in event a or b is m + n

48. You have 6 x-box games and 10 wii games
You have 6 x-box games and 10 wii games. In how many ways can you choose an x-box game or a wii game to play after school?

49. Answer: 16 ways

50. The Fundamental counting principle part 2 and if event A has “ m” outcomes and event b has “ n” different outcomes then the number of outcomes in event a and b is m • n

51. You have 6 x-box games and 10 wii games
You have 6 x-box games and 10 wii games. In how many ways can you choose an x-box game and a wii game to play after school?

52. Answer: 60 ways

53. Definition of probability p(a) = # of outcomes in A # of possible equally likely outcomes WHAT’S THE Probability of drawing a face card?

54. Definition of probability p(a) = # of outcomes in A # of possible equally likely outcomes examPle: Probability of drawing a face card p(face card) = # face cards # cards = 12/52 = 3/13

55. Given 2 six-sided fair dice, What’s the probability of rolling the sum of 7?

56. First, make a sample space listing all the possible outcomes

57. These are the totals: 2,3,4,5,6,7,8,9,10,11,12 but they are not all equally likely… why not???

58. Make a table of outcomes

61. Suppose a family has two children
Suppose a family has two children. list they outcomes in the sample space

62. Bb, bg, gb, gG

63. Bb,bg,gb,gg a) what are we assuming in thinking these four outcomes are equally likely? B) what is the probability a 2-child family has two girls? C) what is the probability there is at least one girl? D) what is the probability both children are the same sex?

64. Bb,bg,gb,gg a) what are we assuming in thinking these four outcomes are equally likely? The chance of having a boy/girl is 50 – 50 and the sexes of babies born in the same family are independent B) what is the probability a 2-child family has two girls? 1/4 C) what is the probability there is at least one girl? /4 D) what is the probability both children are the same sex? 2/4 or 1/2

65. Tonight’s homework read pages 284 – 290 and do page 300 #1,3,4,6,8,10,17,23,