## MTH212 Foundations of Elementary Math 2

### Fun with Fractions.

Notes on Fractions
Winter 2020

### Chapter 8: Probability and Counting

#### § 8.1 Single Stage Experiments

Topics

• 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.