1 / 17
Basic Probability | Problem-Solving and Data Analysis

Basic Probability of Single Events

SAT Problem-Solving and Data Analysis

In this lesson:

  • Calculate probability using
  • Read probability from tables, bar charts, and area models
  • Use the complement and addition rules
Grade 10 SAT Math | Domain 2: Problem-Solving and Data Analysis
Basic Probability | Problem-Solving and Data Analysis

Your Learning Goals for This Lesson

You will be able to:

  1. Calculate
  2. Read probabilities from tables, bar charts, and area models
  3. Use a given probability to find an unknown count
  4. Use the complement rule to find
  5. Apply the addition rule for compound events
Grade 10 SAT Math | Domain 2: Problem-Solving and Data Analysis
Basic Probability | Problem-Solving and Data Analysis

Warm-Up: Conversions and Answer Formats

Ten-second check: write as a decimal and a percent. ;

Answer formats:

  • Multiple choice: match the form of the options
  • Student-produced response: a fraction or a decimal, no percent sign
Grade 10 SAT Math | Domain 2: Problem-Solving and Data Analysis
Basic Probability | Problem-Solving and Data Analysis

Probability Is a Ratio: Favorable Over Total

A bag has 4 red, 3 blue, and 5 green marbles. One is drawn at random.

Grade 10 SAT Math | Domain 2: Problem-Solving and Data Analysis
Basic Probability | Problem-Solving and Data Analysis

Reading Probability from Two-Way Tables

Two-way frequency table: Grade vs subject preference, 200 students total

Recall: grand total 200; row totals 80 and 120.

Chosen from all 200:

Grade 10 SAT Math | Domain 2: Problem-Solving and Data Analysis
Basic Probability | Problem-Solving and Data Analysis

Working Backward: Probability to Count

Reverse: a student is chosen at random from 200, and . How many are in Grade 9?

Count = probability × total.

Grade 10 SAT Math | Domain 2: Problem-Solving and Data Analysis
Basic Probability | Problem-Solving and Data Analysis

Bar Chart: Heights Are the Counts

Bar chart of the favorite season of 80 students: winter 12, spring 18, summer 30, fall 20

Grade 10 SAT Math | Domain 2: Problem-Solving and Data Analysis
Basic Probability | Problem-Solving and Data Analysis

Area Model: Areas Replace Counts

A 10 by 6 rectangle containing a shaded 4 by 3 rectangle

A point is chosen at random in the rectangle.

Grade 10 SAT Math | Domain 2: Problem-Solving and Data Analysis
Basic Probability | Problem-Solving and Data Analysis

The Complement Rule: Finding P(not A)

Die:

Table:

Faster than adding .

Grade 10 SAT Math | Domain 2: Problem-Solving and Data Analysis
Basic Probability | Problem-Solving and Data Analysis

The Addition Rule for Overlapping Events

Venn diagram showing two overlapping circles A and B, overlap shaded twice

Cannot overlap? :

Grade 10 SAT Math | Domain 2: Problem-Solving and Data Analysis
Basic Probability | Problem-Solving and Data Analysis

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: , too large.

Grade 10 SAT Math | Domain 2: Problem-Solving and Data Analysis
Basic Probability | Problem-Solving and Data Analysis

Check Your Answer: Count and Range

People count: Grade 9 (80) + Grade 10 science (70) = 150 ✓

Range: Grade 10 or science without subtracting: . Correct: .

is below 1 and slips through: count people.

"And" is one cell:

Grade 10 SAT Math | Domain 2: Problem-Solving and Data Analysis
Basic Probability | Problem-Solving and Data Analysis

SAT Problem 1: Choose the Right Denominator

From all 200 students, one is chosen. What is ?

A) B) C) D)

Answer: C. . Choice A uses the row total, 80.

Grade 10 SAT Math | Domain 2: Problem-Solving and Data Analysis
Basic Probability | Problem-Solving and Data Analysis

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.

Grade 10 SAT Math | Domain 2: Problem-Solving and Data Analysis
Basic Probability | Problem-Solving and Data Analysis

SAT Problem 3: Addition Rule and Entry Field

From all 200 students, one is chosen. ?

The entry field takes 5 characters: does not fit. Enter or .

Grade 10 SAT Math | Domain 2: Problem-Solving and Data Analysis
Basic Probability | Problem-Solving and Data Analysis

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

Grade 10 SAT Math | Domain 2: Problem-Solving and Data Analysis
Basic Probability | Problem-Solving and Data Analysis

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.

Grade 10 SAT Math | Domain 2: Problem-Solving and Data Analysis