Probability and Odds

BIG IDEAS: (taken from “Big Ideas by Dr. Small”):

1. Real-world situations can be represented using probabilities.

2. Probability can be used to predict outcomes.

3. Experimental probability and theoretical probability may differ due to chance.

STUDENT LEARNING GOALS:

GOAL #1: I can determine the theoretical probability of simple events.

• VIDEO: Finding Outcomes of Single Events (Source: kolumath)

• VIDEO: Introduction to Theoretical Probability (Source: Khan Academy)

• VIDEO: Determining Theoretical Probability of Single Events (Source: Khan Academy)

• VIDEO: Intuitive Sense of Probability (Source: Khan Academy)

• VIDEO: Making Predictions from Theoretical Probability (Source: mrmaisonet)

• QUIZ: Predicting Probabilities (Source: Nelson Education)

• QUIZ: Calculating Theoretical Probability of Single Events (Source: Nelson Education)

• GAME: Probability Continuum (Source: BiteSize Maths)

GOAL #2: I can determine the theoretical probability of compound events.

• VIDEO: Using Tree Diagrams to Find Possible Outcomes (Source: MashUp Math)

• VIDEO: Using Tree Diagrams for Multiple Coin Flips (Source: Khan Academy)

• VIDEO: Solving a Problem using a Matrix Table (Source: MashUp Math)

• VIDEO: Die Rolling Problem (Source: Khan Academy)

• VIDEO: Finding Probability of Complex Events using an Area Model (Source: Sophia.org)

• VIDEO: The Last Banana – A Thought Experiment (Source: TED-Ed)

• VIDEO: Permutations – Code Breaker (Source: Khan Academy)

• QUIZ: Determining Possible Outcomes of Compound Events (Source: Nelson Education)

• QUIZ: Calculating Probability (Source: Nelson Education)

• QUIZ: Using Tree Diagrams to Find Probabilities (Source: Nelson Education)

• QUIZ: Finding Probability of Compound Events (Source: Nelson Education)

• QUIZ: Determining Theoretical Probability (Source: Nelson Education)

• GAME: Probability Circus (Source: hbschool)

GOAL #3: I can determine the relative frequency with and without running simulations.

• VIDEO: Calculating Experimental Probability (Source: MathHelp.com)

• VIDEO: Making Predictions from Relative Frequencies (Source: Khan Academy)

• QUIZ: Comparing Theoretical and Experimental Probability (Source: Nelson Education)

• QUIZ: Applying Probabilities (Source: Nelson Education)

CURRICULUM EXPECTATIONS:

• organize into intervals a set of data that is spread over a broad range (e.g., the age of respondents to a survey may range over 80 years and may be organized into ten-year intervals);

• read, interpret, and draw conclusions from primary data (e.g., survey results, measurements, observations)

• compare, through investigation, the theoretical probability of an event (i.e., the ratio of the number of ways a favourable outcome can occur compared to the total number of possible outcomes) with experimental probability, and explain why they might differ (Sample problem:Toss a fair coin 10 times, record the results, and explain why you might not get the predicted result of 5 heads and 5 tails.);

• determine, through investigation, the tendency of experimental probability to approach theoretical probability as the number of trials in an experiment increases, using class-generated data and technology-based simulation models (Sample problem: Compare the theoretical probability of getting a 6 when tossing a number cube with the experimental probabilities obtained after tossing a number cube once, 10 times, 100 times, and 1000 times.);

• identify the complementary event for a given event, and calculate the theoretical probability that a given event will not occur (Sample problem: Bingo uses the numbers from 1 to 75. If the numbers are pulled at random, what is the probability that the first number is a multiple of 5? is not a multiple of 5?).