Mathematics

THE ONTARIO CURRICULUM, GRADES 11 AND 12 | Mathematics Grade 12, Workplace Preparation1.8 gather, interpret, and describe informationabout applications of data management in theworkplace and in everyday life2. Investigating ProbabilityBy the end of this course, students will:2.1 determine the theoretical probability of anevent (i.e., the ratio of the number offavourable outcomes to the total number ofpossible outcomes, where all outcomes areequally likely), and represent the probabilityin a variety of ways (e.g., as a fraction, as apercent, as a decimal in the range 0 to 1)2.2 identify examples of the use of probabilityin the media (e.g., the probability of rain, ofwinning a lottery, of wait times for a serviceexceeding specified amounts) and variousways in which probability is represented(e.g., as a fraction, as a percent, as a decimalin the range 0 to 1)2.3 perform simple probability experiments (e.g.,rolling number cubes, spinning spinners, flippingcoins, playing Aboriginal stick-and-stonegames), record the results, and determine theexperimental probability of an event2.4 compare, through investigation, the theoreticalprobability of an event with the experimentalprobability, and describe how uncertaintyexplains why they might differ (e.g., “I knowthat the theoretical probability of getting tailsis 0.5, but that does not mean that I willalways obtain 3 tails when I toss the coin6 times”; “If a lottery has a 1 in 9 chanceof winning, am I certain to win if I buy9 tickets?”)2.5 determine, through investigation using classgenerateddata and technology-based simulationmodels (e.g., using a random-numbergenerator on a spreadsheet or on a graphingcalculator), the tendency of experimentalprobability to approach theoretical probabilityas the number of trials in an experimentincreases (e.g., “If I simulate tossing a coin1000 times using technology, the experimentalprobability that I calculate for getting tails inany one toss is likely to be closer to the theoreticalprobability than if I simulate tossingthe coin only 10 times”)Sample problem: Calculate the theoreticalprobability of rolling a 2 on a number cube.Simulate rolling a number cube, and use thesimulation to calculate the experimentalprobability of rolling a 2 after 10, 20, 30, …,200 trials. Graph the experimental probabilityversus the number of trials, and describe anytrend.2.6 interpret information involving the use ofprobability and statistics in the media, anddescribe how probability and statistics canhelp in making informed decisions in avariety of situations (e.g., weighing the riskof injury when considering different occupations;using a weather forecast to planoutdoor activities; using sales data to stocka clothing store with appropriate stylesand sizes)Sample problem: A recent study on youthgambling suggests that approximately 30%of adolescents gamble on a weekly basis.Investigate and describe the assumptionsthat people make about the probability ofwinning when they gamble. Describe otherfactors that encourage gambling and problemsexperienced by people with a gamblingaddiction.150