Unit 11 · 9th Grade Mathematics

Data Analysis
& Probability.

Two-way tables, probability, expected value, and making statistical decisions.

Start studyingTopic B: Probability

Unit 11 — Lesson Video

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Topic A: Two-Way Tables & Categorical Data

Lessons 1–4 · Analyzing categorical data with two-way frequency tables.

01–04 — Lessons 1–4

Two-Way Frequency Tables

Two-way tables display counts or frequencies for two categorical variables simultaneously.

  • Joint frequency: count in one specific cell.
  • Marginal frequency: row or column total.
  • Conditional frequency: proportion within a row or column.
  • Used to identify associations between categorical variables.
  • Relative frequency = count ÷ total.
In a survey: 30 students like math AND science, 50 total like math → P(science|math) = 30/50 = 0.6.
Practice — Lessons 1–4
Q1 · Multiple Choice

In a two-way table, a marginal frequency is:

Q2 · Short Answer

15 students passed both tests out of 25 who passed Math. P(passed Science | passed Math) = ?

Topic B: Probability

Lessons 5–8 · Theoretical, experimental, and compound probability.

05–08 — Lessons 5–8

Probability Fundamentals

  • Theoretical probability: P(event) = favorable outcomes / total outcomes.
  • Experimental probability: from actual trials — may differ from theoretical.
  • P(A) is between 0 and 1. P(certain) = 1. P(impossible) = 0.
  • Complement rule: P(not A) = 1 − P(A).
  • Independent events: P(A and B) = P(A) × P(B).
  • Mutually exclusive: P(A or B) = P(A) + P(B).
Flip two coins. P(both heads) = (1/2)(1/2) = 1/4. P(at least one head) = 1 − P(no heads) = 3/4.
Practice — Lessons 5–8
Q3 · Multiple Choice

P(A) = 0.3 and P(B) = 0.5. If A and B are independent, P(A and B) = ?

Q4 · Multiple Choice

A bag has 4 red and 6 blue marbles. P(not red) = ?

09–11 — Lessons 9–11 (Extended)

Expected Value & Simulation

Expected value uses probability to find the average outcome over many trials.

  • Expected value: E(X) = Σ [x · P(x)] — sum of each value times its probability.
  • Used in games, insurance, and decision-making.
  • Simulation: model a probability experiment using random numbers.
  • The law of large numbers: as trials increase, experimental → theoretical probability.
  • Fair game: expected value = 0 (or fair price for each player).
Roll a die: P(each face) = 1/6. E(X) = (1+2+3+4+5+6)/6 = 3.5
Practice — Lessons 9–11
Q5 · Multiple Choice

In a game, you win $5 with P=0.4 and lose $3 with P=0.6. Expected value = ?

Q6 · Multiple Choice

The Law of Large Numbers states: