## D2. Probability

### Specific Expectations

#### Probability

D2.1

use fractions to express the probability of events happening, represent this probability on a probability line, and use it to make predictions and informed decisions

**probability line displaying the****likelihood****of various events for an experiment involving rolling one six-sided die:**

- The probability of events is measured in numeric values ranging from 0 to 1.
- Fractions can be used to express the probability of events across the 0 to 1 continuum.

*Note*

- Have students make connections between the words to describe the likelihood of events (from Grade 4) and possible fractions that can be used to represent those benchmarks on the probability line.

Support students in making connections between fractions and words to describe the likelihood of events. Have them draw a benchmark probability line by marking 0 and 1 at opposite ends and labelling them as “impossible” and “certain”, respectively. Next, ask them to mark three fractions on the probability line that could be used to represent “equally likely”, “unlikely”, and “likely”. Talk about what the fraction must be for “equally likely” and, similarly, what good benchmarks might be for “unlikely” and “likely”. As students work with probability, they can use this probability line and the benchmarks to make predictions based on the likelihood of events expressed as fractions.

D2.2

determine and compare the theoretical and experimental probabilities of an event happening

**probability experiments:**- throw a paper cup up in the air and determine how it will land (side, top, or bottom) 10 times
- roll a single die 20 times
- spin a spinner 12 times

**determining the theoretical probability:**- rolling a single die:
- There are six possible outcomes: 1, 2, 3, 4, 5, 6.
- The theoretical probability of rolling a 2 is .
- The theoretical probability of rolling a number greater than 4 is .

- rolling a single die:
**comparing experimental probability with theoretical probability:**- The more trials done in an experiment, the closer the experimental probability will be to the theoretical probability.
- Increase the number of trials by:
- continuing the experiment over multiple trials, or
- combining classmates’ experimental results

- The more trials done in an experiment, the closer the experimental probability will be to the theoretical probability.
- The sum of the probabilities of all possible outcomes is 1.
- The probability of an event can be used to predict the likelihood of that event happening again in the future.

*Notes*

- “Odds in favour” is a comparison of the probability that an event will occur to the probability that the event will not occur (complementary events). For example, the odds in favour of rolling a 6 are :, which can be simplified to 1:5 since the fractions are both relative to the same whole.

As an introduction to probability experiments, have students do experiments in which the outcomes of each trial are equally likely to happen. For example, give each pair of students one die and have them predict all the possible outcomes if they roll the die once (1, 2, 3, 4, 5, or 6), and predict the likelihood of rolling a 3, a 5, or a 2. Now ask them to predict what might happen if they rolled the die 30 times. Guide them to the understanding that theoretically, each number would come up five times.

Ask each pair to record the results for 30 rolls of their die. Once the trials are completed, ask students to compare their result (experimental) with what they had predicted (theoretical).

Have students repeat the experiment. Ask them to compare the two data sets. Ask them what they think would happen if they put their two data sets together. Have them combine the data sets, and ask what they notice now.

Ask what they think would happen if all the student pairs combined their results. Guide students to an understanding that the greater the number of trials, the closer the experimental probability will be to the theoretical probability.