D2.1 Use fractions, decimals, and percents to express the probability of events happening, represent this probability on a probability line, and use it to make predictions and informed decisions.
Activity 1: Comparison of Experimental and Theoretical Probabilities
Describe to students a probability experiment in which all outcomes are equally likely, such as tossing a coin, rolling a die, spinning a spinner whose sectors have the same area, or drawing a marble from a bag containing the same number of marbles of each colour.
Divide students into teams of two and provide each team with a copy of Appendix 6.4. Help students complete the Possible outcomes section. For example, if the experiment is done using a coin, the possible outcomes are heads and tails.
Have each team perform the experiment 100 times, recording the frequency of the results in Appendix 6.4. Next have students determine their relative frequencies as a fraction, and as a decimal (to the nearest thousandth). Each team must then simulate the experiment 400 times using code or a digital tool and add the results to the previous 100 results so that they have frequencies corresponding to 500 trials. Alternatively, have students combine their results.
Then, each team must repeat the experiment 500 times using the same simulation to obtain frequencies corresponding to 1000 trials.
Following the experiment, ask each team to indicate how close the results of their experiment at each of the three steps are to the theoretical probability. Encourage students to make connections between the number of trials, the frequency of each outcome, and the theoretical probability.
Source: translated from Guide d’enseignement efficace des mathématiques, de la 4e à la 6e année, Traitement des données et probabilité, p. 237-238.
Activity 2: Represent a Probability on a Probability Line
Place fractions, decimals and percents on the following probability line.
\(0.75;\ 0\%;\ \frac{1}{4};\ \frac{1}{2};\ 1;\ 10\%;\ 0.91 \)
Activity 3: Make Predictions Using Probability
Present the following situation to the students.
Antonio's parents pick him up after school 75% of the time. Given that there are 20 school days in February, how many times will Antonio have to take the bus during that month? What is your prediction? Explain your reasoning.