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Probability Expectation Study Guide

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MEP Y9 Practice Book A1216 Probability6.1 The Probability ScaleProbabilities are given on a scale of 0 to 1, as decimals or as fractions; sometimesprobabilities are expressed as percentages using a scale of 0% to 100%,particularly on weather forecasts.0 This is the probability of something that is impossible.1 This is the probability of something that is certain.12This is the probability of something that is as likely to happenas it is not to happen.Example 1Decide whether or not each of the statements below is reasonable.(a) The probability that it will snow on Christmas Day in London is 0.9.(b) The probability that you will win a raffle prize is 0.5.(c) The probability that you will go to bed before midnight tonight is 0.99.(d) The probability that your pocket money is doubled tomorrow is 0.01.Solution(a) This is not reasonable as the probability given is much too high. It veryrarely snows in London in late December, so the probability should be closeto 0.(b) This probability is far too high. You would need to have bought half of allthe tickets sold to obtain this probability, so this statement is not reasonable.(c) This is a reasonable statement as it is very likely that you will go to bedbefore midnight, but not certain that you will.(d) This is a reasonable statement, as it is very unlikely that your pocket moneywill be doubled tomorrow, but not totally impossible.Example 2On a probability scale, mark and estimate the probability that:(a) it will rain tomorrow,(b) England will win their next football match,(c) someone in your class has a birthday tomorrow.MEP Y9 Practice Book A122Solution(a) This will depend on the time of year and the prevailing weather conditions.During a dry spell in summer,0 0.5 1During a wet spell in winter,0 0.5 1(b) Based on their recent form, it is reasonable to say that England are slightlymore likely to draw or lose their next match than to win it, so an estimatewould be a little less than 0.5.0 0.5 1(c) The probability of this will be fairly small, as you can expect there to beabout 2 or 3 birthdays per month for pupils in a class of about 30 pupils.0 0.5 1Exercises1. Describe something that is:(a) very unlikely, (b) unlikely,(c) likely, (d) very likely.2. State whether or not each of the statements below is reasonable.(a) The probability that there will be a General Election next year is 0.2.(b) The probability that England will win the next football World Cup is 0.8.(c) The probability that it will not rain tomorrow is 0.9.(d) The probability that your school will be hit by lightning in the nextweek is 0.1.6.1MEP Y9 Practice Book A1233. (a) List the things described, in order, with the most likely first.A You travel on a bus that breaks down on the way home from school.B Your pocket money is increased during the next two weeks.C You enjoy your school lunch tomorrow.D You have already had a birthday this year.(b) Mark estimates of the probabilities of each of these on a copy of theprobability scale similar to the one below:0 0.5 14. Explain why the probability that you will be the first person to walk on themoon is zero.5. Describe something that has a probability of zero.6. (a) Do you agree that the probability that you will not be abducted byaliens in the next 24 hours is 1 ?(b) Explain why.7. Describe something that has a probability of 1.8. When you toss a fair coin, the probability of obtaining a head is 12 and theprobability of obtaining a tail is 12.Describe something else that has a probability that is equal to or close to 12.9. A packet of sweets contains mostly red sweets, a few green sweets and onlyone yellow sweet. You take a sweet at random from the packet.The events A, B, C and D are listed below.A You take a yellow sweet.B You take a green sweet.C You take a red sweet.D You take a blue sweet.(a) Write these outcomes in order of probability, with the most likely first.(b) Mark the probability of each outcome on a scale similar to the one below.0 0.5 1MEP Y9 Practice Book A12410. The probability that a train is late is 0.1. Which of the following statementsis the most reasonable:A The train is unlikely to be late.B The train is very unlikely to be late.C The train is likely to be late.Explain why you have chosen your answer.11. (a) Joe has these cards:3 9 48 2 7 95Sara takes a card without looking.Joe says: "On Sara's card, is more likely than ."Explain why Joe is wrong.Choose one of the following words and phrases to fill in the gaps in thesentences below:Impossible Not Likely Certain Likely It is ............... that the number on Sara's card will be smaller than 10. It is ............... that the number on Sara's card will be an odd number.(b) Joe still has these cards:3 9 48 2 7 95He mixes them up and puts them face down on the table. Then heturns the first card over, like this:5Joe is going to turn the next card over.Copy and complete this sentence: On the next card, ............... is less likely than ............... .The number on the next card could be higher than 5 or lower than 5.Which of the following possibilities is more likely?Higher than 5 Lower than 5 Cannot tellExplain your answer.(KS3/97/Ma/Tier 3-5/P2)6.1MEP Y9 Practice Book A12512. Here are four spinners, labelled P, Q, R and S.(a) Which spinner gives the greatest chance that the arrow will land onplain?(b) Which spinner gives the smallest chance that the arrow will land onshaded?(c) Shade a copy of the spinner shown sothat it is certain that the arrow willland on shaded.(d) Shade a copy of this spinner so thatthere is a 50% chance that the arrowwill land on shaded.(KS2/98/Ma/Tier 4-6/P2)13. Bryn has some bags with some black beads and some white beads. He isgoing to take a bead from each bag without looking.(a) Match the pictures to the statements. The first is done for you.EDCBASRQPKEYPlainShadedStripedMEP Y9 Practice Book A126(i) It is impossible that Bryn will take a black bead from bag D.(ii) It is unlikely that Bryn will take a black bead from bag ..... .(iii) It is equally likely that Bryn will take a black bead or a whitebead from bag ..... .(iv) It is likely that Bryn will take a black bead from bag ..... .(v) It is certain that Bryn will take a black bead from bag ..... .(b) Bryn has 5 white beads in a bag.He wants to make it more likely that he will take a black bead than awhite bead out of the bag.How many black beads should Bryn put into the bag?(c) There are 20 beads altogether in another bag. All


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