Your Learning Goals for This Lesson
You will be able to:
- Calculate
- Read probabilities from tables, bar charts, and area models
- Use a given probability to find an unknown count
- Use the complement rule to find
- Apply the addition rule for compound events
Warm-Up: Conversions and Answer Formats
Ten-second check: write
Answer formats:
- Multiple choice: match the form of the options
- Student-produced response: a fraction or a decimal, no percent sign
Probability Is a Ratio: Favorable Over Total
A bag has 4 red, 3 blue, and 5 green marbles. One is drawn at random.
Reading Probability from Two-Way Tables
Recall: grand total 200; row totals 80 and 120.
Chosen from all 200:
Working Backward: Probability to Count
Reverse: a student is chosen at random from 200, and
Count = probability × total.
Bar Chart: Heights Are the Counts
Area Model: Areas Replace Counts
A point is chosen at random in the rectangle.
The Complement Rule: Finding P(not A)
Die:
Table:
Faster than adding
The Addition Rule for Overlapping Events
Cannot overlap?
Addition Rule Applied: Overlapping Events
From the survey table (200 students),
The 35 Grade 9 science students are counted twice, so subtract them once. Without it:
Check Your Answer: Count and Range
People count: Grade 9 (80) + Grade 10 science (70) = 150 ✓
Range: Grade 10 or science without subtracting:
"And" is one cell:
SAT Problem 1: Choose the Right Denominator
From all 200 students, one is chosen. What is
A)
Answer: C.
. Choice A uses the row total, 80.
SAT Problem 2: Student-Produced Complement
From all 200 students, one is chosen. What is
Answer:
. Enter or .
Either form is accepted; do not type a percent sign.
SAT Problem 3: Addition Rule and Entry Field
From all 200 students, one is chosen.
The entry field takes 5 characters:
Key Takeaways: Basic Probability Rules
- ✓
- ✓ Denominator = the group you select from
- ✓ Complement:
- ✓ Addition: subtract the overlap
Wrong denominator: ask what group you select from
Overlap forgotten: answer too large
What You Will Learn Next
Next lesson: Conditional Probability
You will learn:
: the probability of given that has occurred- How "given that" changes the denominator
- Why
in general
Conditional probability uses the same tables — just a different denominator.