Page 115 - The Ontario Curriculum, Grades 11 and 12: Mathematics, 2007

A. COUNTING AND PROBABILITY OVERALL EXPECTATIONS
By the end of this course, students will:
SPECIFIC EXPECTATIONS
By the end of this course, students will:
1.1 recognize and describe how probabilities are used to represent the likelihood of a result of an experiment (e.g., spinning spinners; draw- ing blocks from a bag that contains different- coloured blocks; playing a game with number cubes; playing Aboriginal stick-and-stone games) and the likelihood of a real-world event (e.g., that it will rain tomorrow, that an accident will occur, that a product will be defective)
1.2 describe a sample space as a set that contains all possible outcomes of an experiment, and distinguish between a discrete sample space as one whose outcomes can be counted (e.g., all possible outcomes of drawing a card or tossing a coin) and a continuous sample space as one whose outcomes can be measured (e.g., all possible outcomes of the time it takes to complete a task or the maximum distance a ball can be thrown)
1.3 determine the theoretical probability, Pi (i.e., a value from 0 to 1), of each outcome of a discrete sample space (e.g., in situations in which all outcomes are equally likely), recognize that the sum of the probabilities of the outcomes is 1 (i.e., for n outcomes,
P1 +P2 +P3 +... +Pn = 1), recognize that the probabilities Pi form the probability distribu- tion associated with the sample space, and solve related problems
Sample problem: An experiment involves rolling two number cubes and determining the sum. Calculate the theoretical probability of each outcome, and verify that the sum of the probabilities is 1.
1.4 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; using dynamic statistical software to simulate repeated trials in an experiment), the tendency of experimental probability to approach theoretical probability as the num- ber of trials in an experiment increases (e.g., “If I simulate tossing two coins 1000 times using technology, the experimental probabil- ity that I calculate for getting two tails on
the two tosses is likely to be closer to the theoretical probability of 14 than if I simulate tossing the coins only 10 times”)
Sample problem: Calculate the theoretical probability of rolling a 2 on a single roll of a number cube. Simulate rolling a number cube, and use the simulation results to calcu- late the experimental probabilities of rolling a 2 over 10, 20, 30, ..., 200 trials. Graph the experimental probabilities versus the number of trials, and describe any trend.
1.5 recognize and describe an event as a set of outcomes and as a subset of a sample space, determine the complement of an event, deter- mine whether two or more events are mutual- ly exclusive or non-mutually exclusive (e.g., the events of getting an even number or
COUNTING AND PROBABILITY
1. solve problems involving the probability of an event or a combination of events for discrete sample spaces;
2. solve problems involving the application of permutations and combinations to determine the probability of an event.
1. Solving Probability Problems Involving Discrete Sample Spaces
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Mathematics of Data Management
MDM4U