Starter 1 4 Good 5 8 Ace 9 12 Awesome 13 Superstar Impossible Certain May Might Probable Chance Possible Unlikely Improbable ID: 1001988
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1. How many words can you find relating to probability? Starter1 – 4 = Good 5 – 8 = Ace 9 – 12 = Awesome13 + = Superstar!
2. ImpossibleCertainMayMightProbableChancePossibleUnlikelyImprobableMoreLessCouldWouldLikelyWon’tPoorEvenGoodDefiniteNever
3. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1likelyunlikelycertainimpossibleeven chance100% chanceno chance75% chance50% chance25% chanceMatch the labels to the correct place on the probability scale
4. Use the words to describe the probabilities of the events below:Impossible?LikelyUnlikelyCertainLikelyEven chanceCertainUnlikelyUnlikelyYou will celebrate your 10th birthday tomorrow.Tomorrow you will have a cold.It will rain tomorrow.You will be struck by lightning tomorrow.You will have something to drink tomorrow.Sometime tomorrow you will watch television.The next person you pass in the corridor will be male.The sun will rise tomorrow morning.Rolling the number six on a dice on one throw. You will still be alive when you are 100.
5. Sometimes words aren’t enough!To be more accurate, we express probability as a numberWe’re mathematicians! How can we be more accurate when talking about probability?
6. The probability that an event will happen is a number between 0 and 1The probability for an event which is CERTAIN = 1The probability for an event which is IMPOSSIBLE = 0Probability can be expressed as a fraction, a decimal or a percentage150.220%
7. Example 1If I had a bag containing an apple and a pear, what is the probability that I will pick out the pear?50%or 0.5or12
8. A box contains 3 bags of salt and vinegar crisps, 4 bags of cheese and onion crisps and 2 bags of beef crisps. One of these bags of crisps is taken from the box at random. Work out the probability that the bag of crisps will be: a) salt and vinegar b) cheese and onion c) beefExample 23/94/92/9
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10. AnswersEventNumber of ways of achieving successNumber of possible outcomesProbabilityThrowing a 216 Throwing a 516 Throwing an odd number36 Throwing more than 3 36 Throwing less than 5 46 Throwing 2 or more 56 Throwing a 7 06 = 0Throwing an even number 36 Throwing less than 7 66 = 1 EventNumber of ways of achieving successNumber of possible outcomesProbabilityThrowing a 216Throwing a 516Throwing an odd number36Throwing more than 3 36Throwing less than 5 46Throwing 2 or more 56Throwing a 7 06Throwing an even number 36Throwing less than 7 66
11. It is impossible that Ethan will take a red sweet from…Bag 4 Bag 2Bag 5Bag 1
12. It is unlikely that Ethan will take a red sweet from…Bag 4 Bag 2Bag 5Bag 1
13. It is even chance that Ethan will take a red sweet from…Bag 4 Bag 2Bag 5Bag 1
14. What is the probability of choosing a red counter from this bag?7/54/127/121/11
15. What is the probability of choosing a yellow counter from this bag?7/54/124/121/12
16. What is the probability of choosing a green counter from this bag?7/54/124/121/12
17. What is the probability of this spinner landing on pink?1/121/602/6
18. What is the probability of this spinner landing on yellow?2/61/32/41/6
19. What is the probability of this spinner landing on light blue?12/63/123/6
20. What is the probability of this spinner NOT landing on pink?03/65/61/6
21. What is the probability of choosing the letter A at random from the wordMATHEMATICS2/123/112/112/9
22. What is the probability of choosing a vowel at random from the wordMATHEMATICS3/113/104/74/11
23. What is the probability of choosing a consonant at random from the wordMATHEMATICS4/117/117/44/7
24. Mutually Exclusive EventsWhat does mutually exclusive mean?Mutually exclusive means “can’t happen at the same time”So, mutually exclusive events are events that cannot happen at the same time
25. Going to Liverpool at 9am tomorrow, or going to Manchester at 9am tomorrowTurning left or turning right For example(You cannot turn left and right at the same time, or be in two places at once!)
26. What is not Mutually ExclusiveTurning left and scratching your head can happen at the same timeKings and Hearts, because you can have a King of Hearts
27. The following statements are mutually exclusive… True or false?
28. Question 1Winning a football matchANDLosing the same football matchTrue
29. Question 2Having pizza for dinnerANDHaving ice cream for puddingFalse
30. Question 3Getting the busANDMissing the busTrue
31. Question 4Watching a comedy DVDANDWatching a romance DVDFalse
32. Question 5Being awakeANDBeing asleepTrue
33. Question 6Rolling a 2 on a diceANDRolling a number less than 3False
34. Question 7A traffic light being redANDA traffic light being greenTrue
35. Question 8A baby being a boyANDThe same baby being a girlTrue
36. Question 9Randomly picking a dog from the poundANDThe dog being brownFalse
37. Question 10Me not winning the lotteryANDMy friend not winning the lotteryFalse
38. Probability BingoAim: Full HouseGrid: 9 GridPlay: Calculate probability& cross it off
39. Numbers to Use¼ 0.42 5/6 12%0.35 ½ 7/15 0.6230% 13/20 0.4 57%¾ 1/3 55% 0.34
40. Probability of scoring less than 6 on a normal dice
41. The probability that I will set homework is 0.66. What is the probability I will not set homework?
42. The chance of picking a girl from a group of 3 girls and 7 boys.
43. There are 4 white beads, 2 red beads, 1 green bead and 8 blue beadsWhat is the probability that the bead I pick is NOT blue?
44. The chance of getting 2 heads when 2 coins are flipped.
45. The probability that I choose a girl to answer a question is 0.58 what is the probability I choose a boy?
46. Tonight I can go to the cinema, visit a friend or stay at home.I am equally likely to do each thingWhat is the probability I stay at home?
47. What is the probability of getting a prime number when a normal dice is thrown?
48. I have red, green and black socksThe probability I wear red socks is 0.15The probability I wear green socks is 0.23I am going to wear socks. What is the probability I wear black socks?
49. At a running club 25% of the runners have run a marathon.What is the probability a runner picked at random has not run a marathon?
50. A box of chocolates has 5 strawberry creams, 4 coffee creams, 9 caramels and 2 toffee dreams.What is the probability that I pick a coffee cream or a caramel?
51. In an experiment a drawing pin lands point down 9 times out of 20.What is the experimental probability that the pin will land point up?
52. The probability that it rains tomorrow is 0.43. What is the probability that it will NOT rain?
53. In a year group of 200 students 70 are left handed. What is the probability that a randomly picked student will be left handed?
54. In a group of 50 teachers 6 are mathematicians.What is the probability that a teacher picked at random will be a mathematician?
55. I observe 100 cars. I see 40 red cars. Use relative frequency to estimate the probability that the next car I see will be red.
56. Exhaustive EventsWhat does exhaustive mean?The probabilities of all possible outcomes add up to 1.
57. Total: =1The probability of getting a 1 is The probability of getting a 2 is The probability of getting a 3 is The probability of getting a 4 is The probability of getting a 5 is The probability of getting a 6 is Example 1
58. Flavour of crispSalt & Vinegar Cheese & onionBeef ProbabilityFlavour of crispSalt & Vinegar Cheese & onionBeef ProbabilityA box contains 3 bags of salt and vinegar crisps, 4 bags of cheese and onion crisps and 2 bags of beef crisps. One of these bags of crisps is taken from the box at random. What is the probability they are beef?Example 21 – ( + ) =
59. In a survey during walk to school week, all the pupils at Winsford Academy either cycle, walk, come by bus or still come in a car. The probabilities they travel each way are below. What’s the probability they come by bus?Example 3P(bus) = 1 – (0.36 + 0.52 + 0.06)Method of TravelCycleWalkBusCarProbability0.360.520.06= 0.06
60.
61. Answers – Q1 & 2EventM or N?E?Tossing a head with a coin / Tossing a tail with a coinME (H or T)Throwing a number less than 3 with a dice / Throwing a number greater than 3 with a diceMDrawing a Spade from a pack of cards / drawing an Ace from a pack of cardsNDrawing a Spade from a pack of cards / Drawing a red card from a pack of cardsM(Choosing from a group of three girls and two boys): Choosing two girls / choosing two boysNDrawing a red card from a pack of cards / drawing a black card from a pack of cardsMEWinning a football match / Drawing a football matchMEating toast for breakfast / Eating chips for dinnerN
62. Answers – Q3, 4, 5 & 6Question 3P (not h) = 0.7P (not h) = 0.48P (not h) = 0.79P (not h) = 75%P (not h) = 2%P (not h) = 44.5%P (not h) = 3/5P (not h) = 3/15Question 40.24Question 5P (purple) = 0.1P (purple) = 0.2P (purple) = 4%P (purple) = 7/20Question 6P (3) = 3/8P (red) = 1/8i) M ii) N iii) M iv) M
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64. Which horse is most likely to win?Why?Are there any horses that definitely won’t win?How do you know?
65. Which horse do you think will win? Play now with the person next to you.
66. +234567345678456789567891067891011789101112From this sample space diagram we can see that there are 36 possible outcomes when two dice are thrown.Six of these have a total of 7.77777P(7) =6367
67. How many different combinations could I have?What is the probability of choosing a red t-shirt? I am choosing an outfit…
68. Trousers BlueBlackGreyOrangeT-ShirtRed Blue Black White So the probability of choosing a red t-shirt = 4 16Putting it in to a sample space diagram makes it a lot easier to calculate the probability
69. Trousers BlueBlackGreyOrangeT-ShirtRed Blue Black White Now on whiteboards…As a fraction work out the probability of:(a) Choosing a white t-shirt with either blue or grey trousers(b) Not choosing orange or blue trousers1 81 2
70. AnswersQuestion 11/121/120Question 23/162/164/164/16Question 315/253/2512/257/254/25Question 48/3604/3624/36Question 52/246/247/241/245/24
71. Starter – True or FalseYou are equally likely to get a heads or tails when flipping a fair coinYou are more likely to get an even number when rolling a fair dieThe probability of landing on a 1 on the spinner is 1/42543The probability of picking a red card is 2/3The probability of not picking a black card is 4/6The probability of choosing an ‘A’ from is 2/10TrueFalseTrueFalseTrueFalse
72. Probability TreesThe probabilities for each event are shown along the arm of each branch and they sum to 1.Ends of first and second level branches show the different outcomes.
73. blackgreenFirst ChoiceSecond ChoiceblackgreenblackgreenRebecca has nine coloured beads in a bag. Four of the beads are black and the rest are green. She removes a bead at random from the bag and notes the colour before replacing it. She then chooses a second bead. Draw a tree diagram showing all possible outcomes. Calculate the probability that Rebecca chooses: (i) 2 green beads (ii) A black followed by a green bead.
74. redblueFirst ChoiceSecond ChoiceredblueredbluePeter has ten coloured cubes in a bag. Three of the cubes are red and seven are blue. He removes a cube at random from the bag and notes the colour but does not replace it. He then chooses a second cube at random. Draw a tree diagram showing all possible outcomes. Calculate the probability that Peter chooses: (i) 2 red cubes (ii) A blue cube followed by a red cube.
75. MilkDarkFirst PickSecond PickMilkDarkMilkDarkThe ‘And’ and ‘Or’ RulesCalculate the probability of picking one milk chocolate and one dark chocolate in any order. Milk AND dark OR dark AND milk= 18 x 12 + 12 x 18 30 29 30 29= 432 870
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77. ExtensionThere are 4 blackcurrant sweets, 3 apple sweets and 4 strawberry sweets in a bowl.I pick two sweets (one after the other).What is the probability that I pick two sweets of the same flavour?
78. Answers24492442 2 16 5890 90 90
79. Pair ActivityFirst CardSecond Card£10You are running a stall at a carnival using the pack of cards, any heart wins. At £10 a go, what would you make prize y in order to make a profit, and to make the game enticing? NotNotNot£y£3£0£3¼ ¼ ¼ ¾ ¾ ¾
80. PlenarySummarise in a text message (160 characters) what the key learning points are from today’s lesson.