Mathematics
Grade 10
15 min
Compound events - find the number of outcomes by counting
Compound events - find the number of outcomes by counting
What you'll learn
- Identify the domain and range restrictions necessary to define the inverse trigonometric functions (arcsin(x), arccos(x), arctan(x)) and explain why these restrictions are required for the inverse functions to exist.
- Solve equations involving inverse trigonometric functions, expressing solutions in exact form (using radians) when possible, and approximating solutions to a specified number of decimal places when necessary, demonstrating proficiency in algebraic manipulation and applying the properties of inverse functions.
- Evaluate expressions involving compositions of trigonometric functions and their inverses (e.g., sin(arctan(x)), cos(arcsin(x))), simplifying the expressions to algebraic functions in terms of x, demonstrating an understanding of the relationship between trigonometric functions and their inverses.
- Apply inverse trigonometric functions to model and solve real-world problems involving angles of elevation/depression, navigation, and other applications where the unknown is an angle, interpreting the solutions in the context of the problem.
- Evaluate composite trigonometric and inverse trigonometric expressions (e.g., sin(arctan(x)), cos(arcsin(x))), simplifying the expressions using trigonometric identities and inverse function properties, achieving at least 75% accuracy on a problem set.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Define a compound event and distinguish it from a simple event.
Construct organized lists to represent the sample space of a compound event.
Create tree diagrams to visualize and count the total number of outcomes for a compound event.
State and apply the Fundamental Counting Principle to efficiently calculate the number of outcomes.
Solve multi-step real-world problems by breaking them down into a sequence of simple events.
Interpret the sample space of a compound event to answer specific questions about outcomes.
How many different pizza combinations can you create with 3 crusts, 2 sauces, and 5 toppings? 🍕 Let's find out without listing them all!
This tutorial will introduce you to compound events, which are made up of two or more simple events....
2
Key Concepts & Vocabulary
TermDefinitionExample
OutcomeA single possible result of an experiment or action.When rolling a standard six-sided die, one possible outcome is rolling a 4.
Sample SpaceThe set of all possible outcomes of an experiment.The sample space for flipping a coin is {Heads, Tails}.
Simple EventAn event consisting of only one outcome.Choosing the color blue from a set of colored pencils.
Compound EventAn event that consists of two or more simple events happening in sequence or together.Flipping a coin AND rolling a die. The outcome (Heads, 4) is one result of this compound event.
Organized ListA systematic method of listing all possible outcomes of a compound event.For flipping a coin twice, the organized list is: HH, HT, TH, TT.
Tree DiagramA diagram that uses branches to show all possible outcom...
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Core Formulas
The Fundamental Counting Principle (Two Events)
Total Outcomes = m × n
If a first event can occur in 'm' ways and a second event can occur in 'n' ways, you can find the total number of outcomes for the compound event by multiplying m and n. This is the most efficient way to count outcomes.
The Generalized Fundamental Counting Principle
Total Outcomes = n_1 × n_2 × n_3 × ... × n_k
If a compound event consists of a sequence of 'k' events, and the first event has n_1 outcomes, the second has n_2 outcomes, and so on, the total number of outcomes is the product of the number of outcomes of each individual event.
4 more steps in this tutorial
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Challenging
A car can be purchased in one of 5 colors (Red, Black, White, Silver, Blue), with or without a sunroof, and with one of 3 different engine types (Standard, Turbo, Sport). The Sport engine is only available for Red or Black cars. How many different car configurations are possible?
A.30
B.24
C.18
D.12
Challenging
A student council of 3 members (President, Vice President, Treasurer) is to be elected from a group of 6 candidates. No candidate can hold more than one position. How many different ways can the council be formed?
A.18
B.216
C.30
D.120
Easy
According to the tutorial, which of the following best defines a 'compound event'?
A.single possible result of an experiment.
B.An event that consists of two or more simple events.
C.The set of all possible outcomes of an experiment.
D.An event that has a 100% chance of occurring.
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What grade level is "Compound events - find the number of outcomes by counting"?
Compound events - find the number of outcomes by counting is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Compound events - find the number of outcomes by counting?
You'll be able to: Identify the domain and range restrictions necessary to define the inverse trigonometric functions (arcsin(x), arccos(x), arctan(x)) and explain why these restrictions are required for the inverse functions to exist; Solve….
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How many practice questions are included with Compound events - find the number of outcomes by counting?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.