MTH212 Foundations of Elementary Math 2

Fun with Fractions.

Notes on Fractions
Winter 2020

Chapter 8: Probability and Counting

§ 8.1 Single Stage Experiments


  • Probability: a measure of our belief that something will happen.
  • Experimental Probability: `P(E)="number of times event E was observed"/"total number of observations"`
  • Theoretical: `P(E)="favorable outcomes"/"total outcomes"`
  • Experiment: a planned operation carried out under controlled conditions
  • Outcome: the result of an experiment
  • Event: any group of outcomes
  • Simple Event: an event that can’t be reduced to other events
  • Sample Space: all possible simple events
  • Certain Events: `P=1`
  • Impossible Events: `P=0`
  • Complementary Events:`P(barE)=1-P(E)`
    Some people use `E'` to reference the complement of `E`
  • BMCC Students
      Athlete Not Total
    Male 90 310 400
    Female 110 490 600
    Total 200 800 1000
  • Student Grades on Midterm Exam
      A B C Total
    Male 3 10 5 18
    Female 6 17 19 42
    Total 9 27 24 60
  • Independent Events: `P(A and B)=P(A)P(B)`
  • Mutually Exclusive Events: `P(A or B)=P(A)+P(B)`
  • NON-Mutually Exclusive Events: `P(A or B)=P(A)+P(B)-P(A and B)`
  • Conditional Probability: `P(A | B)=P(A " knowing " B) = (P(A and B))/(P(B))`
Math Activity: Probability Experiments

Purpose: Explore probability through games.

Materials: Sinner or paper clip and pen.

Considerations: Probability is the ratio of favorable outcomes and all outcoms.

`P(E)="number of times event E was observed"/"total number of observations"`

Part 1: Spinners

Spinner 1

Spinner 2

Spinner 3
  • Find a partner, then each select a different spinner.
  • Make a guess as whether your spinner might win more often over your partners spinner and state why.
  • Spin 20 times each. In a table, record the trial number, your spinner value, your partners spinner value, and whether you won or lost. Your table will have 4 columns and a row for each trial, i.e., at least 20 rows.
  • Use the results from your table to estimate the following probabilities
    1. The probability of getting a ___ =
    2. The probability of getting a ___ =
    3. The probability of getting a ___ =
    4. The probability that you win against your partner.
  • Submit your table and answers to the 5 questions.