Illustration of Understands and applies the basic ideas of probability in the ICLE's Rigor and Relevance Framework
Quadrant C

Each student should roll a regular die 20 times and record the number that comes up after each roll. Consider the following events:

  • A={the number that comes up is even}
  • B={the number that comes up is a factor of 6}
  • C={the number that comes up is at most 4}
  • A union B
  • A ununion B
  • A|C
Each student should find the proportion of numbers in each event. Then, all students should combine their results. Find the class proportions. Then, determine the theoretical probability for each of these events. Discuss the connection between the experimental proportions and the theoretical probabilities.

 Quadrant D

In a trial in Sweden, a parking officer testified to having noted the position of the valve stems on the tires on one side of a car. Returning later, the officer noted that the valve stems were still in the same position. The officer issues a ticket for overtime parking. However, the owner of the car claimed he had moved the car and returned to the same parking place. Who was right? Use probability to justify your answer. (See attached task. LINK)
Quadrant A

Suppose you roll a regular die and see which number comes up. List all the elements in the sample space.
List the elements in each of events A, B, and C, below:
A={the number that comes up is even}
B={the number that comes up is a factor of 6}
C={the number that comes up is at most 4}
Find the probability of these events:
P(A), P(B), P(C), P(A B), P(A union B), P(A|C).
Compare your results with other students in your class. Resolve any differences.

 Quadrant B

The diagram below shows the results of a two-question survey administered to 80 randomly selected students at Highcrest High School.
(See attached diagram. LINK)

  • Of the 2100 students in the school, how many would you expect to play a musical instrument?
  • Estimate the probability that an arbitrary student at the school plays on a sports team and plays a musical instrument. How is this related to estimates of the separate probabilities that a student plays a musical instrument and that he or she plays on a sports team?
  • Estimate the probability that a student who plays on a sports team also plays a musical instrument.