Evidence of Understanding

**explain how the number of trials impacts the accuracy of a prediction**- calculate and analyze the
**experimental probability**of an event- as the number of trials increases, compare the ratio of the number of times an event occurred to the number of trials

- explain how the number of trials affects the relationship between experimental and theoretical probability (i.e. as trials increase, the value of the experimental probability approaches the theoretical probability)
- use experimental
**sample space**and theoretical probability to define the expected**frequency**of an event occurring*Example: If an event occurs ½ of the time, then the expected frequency of an event over 100 trials is 50*

- calculate and analyze the
**analyze relationships between quantities for event spaces and sample spaces within a context**- identify quantities and describe the relationships between quantities
- describe the sample space and
**event space**for a particular event - create and justify a representation for a sample space (list of ordered pairs, a tree diagram, two way frequency tables, Venn diagrams, etc.)
- compare relative strengths and weaknesses for each type of representation (tree diagram, two way frequency table, list of events, Venn diagram, etc)

- compare relative strengths and weaknesses for each type of representation (tree diagram, two way frequency table, list of events, Venn diagram, etc)

**compare experimental and theoretical probabilities**- explain why the probability of an outcome must lie between 0 and 1
- the minimum proportion of size of the event space to the sample space, corresponding to an impossible event, is 0
- the maximum proportion of size of the event space to the sample space, corresponding to a certain event, is 1

- justify that the sum of the probability of all possible,
**mutually exclusive**, events occurring is 1- If two events A and B are
**complementary**then the p(A) = 1 - p(B)

- If two events A and B are
- make connections between event space, sample space, number of trials, experimental and theoretical probabilities
- predict how the number of trials impacts how closely the experimental probability matches the theoretical probability
*Example: if an experiment is performed an infinite number of times, the results of the experiment will exactly match the theoretical probability calculated for the experiment*- optional: consider how many trials of an experiment are reasonable to accurately estimate the probability of an event occurring

- use the theoretical probability of an event to calculate its
**expected value**- Ex: If rolling an even number on the sum of two dice is worth $12 when it comes up, then the expected value of any roll given the probability of an even number is 18/36 × $12 = $6

- explain why the probability of an outcome must lie between 0 and 1

**Note: In this unit, there is no reason to require students to reduce fractions since doing so can potentially make seeing the connection between probability and the sample space harder to see.*

Develop conceptual understanding:

trials, accuracy, prediction, experimental probability, theoretical probability, sample space, frequency, event space, mutually exclusive, complementary, expected value

Supporting terms to communicate:

probability, outcome, Tree Diagram, Two Way Frequency Table, Venn Diagram