Problem 2 Finding the Probability of Independent Events
Suppose you roll a red number cube and a blue number cube. What is the probability that you will roll a 3 on the red cube and an even number on the blue cube?
The probability is
Think
Are the events independent?
Yes. The outcome of rolling one number cube does not affect the outcome of rolling another number cube.
✓ Got It?
- You roll a red number cube and a blue number cube. What is the probability that you roll a 5 on the red cube and a 1 or 2 on the blue cube?
Problem 3 Selecting With Replacement
Games You choose a tile at random from the game tiles shown. You replace the first tile and then choose again. What is the probability that you choose a dotted tile and then a dragon tile?
Because you replace the first tile, the events are independent.
Plan
Why are the events independent when you select with replacement?
When you replace the tile, the conditions for the second selection are exactly the same as for the first selection.
The probability that you will choose a dotted tile and then a dragon tile is
✓ Got It?
- In Problem 3, what is the probability that you randomly choose a bird and then, after replacing the first tile, a flower?
Two events are dependent events if the occurrence of one event affects the probability of the second event. For example, suppose in Problem 3 that you do not replace the first tile before choosing another. This changes the set of possible outcomes for your second selection.
Table of Contents
- 2-1 and 2-2 Solving One- and Two-Step Equations
- 2-3 Solving Multi-Step Equations
- 2-4 Solving Equations With Variables on Both Sides
- 2-5 Literal Equations and Formulas
- 2-6 Ratios, Rates, and Conversions
- 2-7 and 2-8 Solving Proportions and Using Similar Figures
- 2-9 Percents
- 2-10 Change Expressed as a Percent
- 3-1 Inequalities and Their Graphs
- 3-2 Solving Inequalities Using Addition or Subtraction
- 3-3 Solving Inequalities Using Multiplication or Division
- 3-4 Solving Multi-Step Inequalities
- 3-5 Working With Sets
- 3-6 Compound Inequalities
- 3-7 Absolute Value Equations and Inequalities
- 3-8 Unions and Intersections of Sets
- Chapter 1 Foundations for Algebra
- Chapter 2 Solving Equations
- Chapter 3 Solving Inequalities
- Chapter 4 An Introduction to Functions
- Chapter 5 Linear Functions
- Chapter 6 Systems of Equations and Inequalities
- Chapter 7 Exponents and Exponential Functions
- Chapter 8 Polynomials and Factoring
- Chapter 9 Quadratic Functions and Equations
- Chapter 10 Radical Expressions and Equations
- Chapter 11 Rational Expressions and Functions
- Chapter 12 Data Analysis and Probability