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1 PageMATHEMATICS DEPARTMENTWorkbookYear 9ProbabilityName:Teacher:
2 PageLevel 4 Achievement objectives Investigate situations that involve elements of chance by comparing experimentaldistributions with expectations from models of the possible outcomes, acknowledgingvariation and independence. Use simple fractions and percentages to describe probabilities.ContentsPageContent3Types of probability3How probability is expressed3Vocabulary4Probability line5Experimental probability and relative frequency5Long run relative frequency and expected value8Theoretical probability9Sample spaces10Probability tree diagrams12Venn diagrams
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5 PageLining it upDraw a probability line below with words and fractions and decimals (where 0.0 impossible and 1.0 certain)1. I have a bag containing 8 different coloured tennis balls. There is 4 orange balls, 2 blue balls, and 2red balls. For each of the following questions give your answer in words and in numbers found onthe probability line.a. What is the probability of removing a blue ball?b. What is the probability of removing a yellow ball?c. What is the probability of removing a orange ball?2. This time the bag has 4 orange balls, 2 blue balls, 2 red balls, 1 green ball and 1 pink ball. For eachof the following questions give your answer in words, with your best estimate of the fraction, plusan accurate decimal.a. What is the probability of removing a green ball?b. What is the probability of removing an orange ball?c. What is the probability of removing a blue ball?
6 PageExperimental ProbabilityObjective: to be able to calculate experimental probability and use it to calculate expected resultsStarter questionsWith a fair dice, what is theprobability of rolling:1.2.3.4.5.6.Below are the probabilities ofan event happening, writea1a2an odd numbera number bigger than 4not the number 5a 4 or 3down the probability of thatevent NOT happening.1.1 out 62.11 out 303.0.24.25%5.0.99Work out:1.2.3.4.5.0.2 x 80.3 x 50.5 x 120.11 x 40.25 x 16Main questions1. Simon records the colour of cars going past his house for an hourColourBlueRedYellowWhiteBlackFrequency54173a. What is the probability the next car will be i) blue ii) red iii) Not blackb. How many Red cars would you expect if i) 100 cars went past ii) 60cars went past iii) 120 cars went past2. Sammy throws a drawing pin 200 times and records how it landsPin upPin down16040a. What is the probability the pin will land i) pin up? ii) pin downb. How many pin ups would you expect if the pin was thrown i) 80 timesii)320 times iii) 400 times iv)1000 times3. A group of children are asked to write for their favourite food, andchild is picked at randomStar questionI want to know theprobability of selectinga four letter word fromthe dictionary (or anyother book) if I choosea word from random.a)Design and carryout an experiment tofind the probability offinding a four letterword.b)How many forletter words would Iexpect to select if Ipicked 100 words.c)How can I makethe experiment asFavourite FoodChinesePizzaMexicanNumber of people201618What is the probability the person i) liked Chinese? ii) Didn’t likeMexican best.b. How many people would you expect to like pizza if i) 100 people wereasked ii) 250 people were asked iv) 1000 people were asked?a.accurate as possible.
7 PagePlaying cards experiment
8 PageRelative frequency - Probability
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15 P a g eExpected value1There are 300 cars in a car park. Theprobability that a car is green is 0.1. Howmany cars are expected to be green?233Complete the table of expected values for the probabilities with a sample size of 200of students in a school of 1500 weigh lessthan 50kg.How many children in the school would youexpect to weight less than 50kg?8Probability0.15E(X)4Of 23,000 apples produced in an orchard,53% are sent for export, 37% are solddomestically. The rest are unfit forconsumptiona. How many are sent for export?b. How many are sold domestically?c. How many are unfit for sale?5There are 150 sweets in a bag. 20% are pink,17% are red, the rest are yellow. How manysweets are there of each colour?0.250.380.22
16 P a g eSample Space Diagrams1. Two fair dice are thrown, and the scores are added together.a) Copy and complete the sample space diagram showing all the possible outcomesb) How many outcomes are there altogether?c) What is the most likely score?d) What are the least likely scores?e) Copy and complete the table showing the probabilities of throwing all the scores from 2 to 12f) What is the probability of a score that is:i) bigger than 10 (does not include 10)ii) a square number (1, 4, 9, 16, 25 )iii) between 3 and 7 (not inclusive)iv) a prime number (2, 3, 5, 7, 11, 13 )v) evenvi) a triangle number (1, 3, 6, 10, 15, )
17 P a g e2. The sample space diagram shows the outcomes from throwing 2 dice when the scores are NOT addedtogetherWhat is the probability that:a) the score is a double?b) the score is an even double?c) the score on one dice is twice the score on the other dice?d) at least one of the dice shows a 2?e) at least one of the dice shows a multiple of 3?3. Copy and complete the diagram for the event ‘the difference between the scores when two fair six sideddice are thrown’ i.e. subtract the smaller score from the biggerFor the event described, find the probability that:a) the difference is 1b) the difference is 0c) the difference is 4d) the difference is 6e) the difference is an odd number
18 P a g e4. Two five sided spinners are spun together.a) Draw a sample space diagram showing all the scores you get when the two scores are addedtogether.b) How many outcomes are there?c) Find the probability thati) the total score is 5ii) the total score is an even numberiii) the total score is a ‘double’iv) the total score is less than 75. Two eightsided dice showing the numbers 1 to 8 were thrown at the same time. What is the probabilitythat the PRODUCT (multiplication) of the two dice is a square number?6. Isaac rolls two dice and multiplies both numbers together to give their product. He wants to know theprobability of rolling two dice that will give him a product between 19 and 35. Explain why a sample spacediagram will help him.
19 P a g eTheoretical Probability
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23 P a g eProbability trees
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33 P a g eVenn Diagrams
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Sammy throws a drawing pin 200 times and records how it lands . Pin up 160 Pin down 40 . a. What is the probability the pin will land i) pin up? ii) pin down b. How many pin ups would you expect if the pin was thrown i) 80 times ii)320 times iii) 400 times iv)1000 times 3. A group of children are asked to write for their favourite food, and
