Page 152 - The Ontario Curriculum, Grades 11 and 12: Mathematics, 2007

Grade 12, Workplace Preparation
2. Investigating Probability
THE ONTARIO CURRICULUM, GRADES 11 AND 12 | Mathematics
1.8 gather, interpret, and describe information about applications of data management in the workplace and in everyday life
By the end of this course, students will:
2.1 determine the theoretical probability of an event (i.e., the ratio of the number of favourable outcomes to the total number of possible outcomes, where all outcomes are equally likely), and represent the probability in a variety of ways (e.g., as a fraction, as a percent, as a decimal in the range 0 to 1)
2.2 identify examples of the use of probability in the media (e.g., the probability of rain, of winning a lottery, of wait times for a service exceeding specified amounts) and various ways in which probability is represented (e.g., as a fraction, as a percent, as a decimal in the range 0 to 1)
2.3 perform simple probability experiments (e.g., rolling number cubes, spinning spinners, flip- ping coins, playing Aboriginal stick-and-stone games), record the results, and determine the experimental probability of an event
2.4 compare, through investigation, the theoretical probability of an event with the experimental probability, and describe how uncertainty explains why they might differ (e.g., “I know that the theoretical probability of getting tails is 0.5, but that does not mean that I will always obtain 3 tails when I toss the coin
6 times”; “If a lottery has a 1 in 9 chance of winning, am I certain to win if I buy 9 tickets?”)
2.5 determine, through investigation using class- generated data and technology-based simula- tion models (e.g., using a random-number generator on a spreadsheet or on a graphing calculator), the tendency of experimental probability to approach theoretical probability as the number of trials in an experiment increases (e.g., “If I simulate tossing a coin 1000 times using technology, the experimental probability that I calculate for getting tails in any one toss is likely to be closer to the theo- retical probability than if I simulate tossing the coin only 10 times”)
Sample problem: Calculate the theoretical probability of rolling a 2 on a number cube. Simulate rolling a number cube, and use the simulation to calculate the experimental probability of rolling a 2 after 10, 20, 30, ..., 200 trials. Graph the experimental probability versus the number of trials, and describe any trend.
2.6 interpret information involving the use of probability and statistics in the media, and describe how probability and statistics can help in making informed decisions in a variety of situations (e.g., weighing the risk of injury when considering different occu- pations; using a weather forecast to plan outdoor activities; using sales data to stock a clothing store with appropriate styles and sizes)
Sample problem: A recent study on youth gambling suggests that approximately 30% of adolescents gamble on a weekly basis. Investigate and describe the assumptions that people make about the probability of winning when they gamble. Describe other factors that encourage gambling and prob- lems experienced by people with a gambling addiction.
150