The mathematical purpose of this lesson is to describe and use the sample space for chance experiments to calculate probabilities for compound events. The work of this lesson connects to previous work because students made connections to prior knowledge about probability and used probability to interpret data. The work of this lesson connects to upcoming work because students will use two-way tables and relative frequency tables to determine probabilities for some events. When students choose to use an organized list, table, or tree diagram to determine the sample space, they are using appropriate tools strategically (MP5).
- Create (in writing and using other representations) and coordinate (orally and in writing) different representations for recording sample space for chance experiments.
- Use organized lists, tables, and tree diagrams to calculate probabilities for compound events.
- Let’s look closer at sample spaces.
- I can create organized lists, tables, and tree diagrams and use them to calculate probabilities.
A chance experiment is something you can do over and over again, and you don’t know what will happen each time.
For example, each time you spin the spinner, it could land on red, yellow, blue, or green.
An event is a set of one or more outcomes in a chance experiment. For example, if we roll a number cube, there are six possible outcomes.
Examples of events are “rolling a number less than 3,” “rolling an even number,” or “rolling a 5.”
An outcome of a chance experiment is one of the things that can happen when you do the experiment. For example, the possible outcomes of tossing a coin are heads and tails.
The probability of a chance event is a number from 0 to 1 that expresses the likelihood of the event occurring, with 0 meaning it will never occur and 1 meaning it will always occur.
The sample space is the list of every possible outcome for a chance experiment.
For example, the sample space for tossing two coins is:
heads-heads tails-heads heads-tails tails-tails