Mathematics
Grade 10
15 min
Compound events: find the number of outcomes
Compound events: find the number of outcomes
What you'll learn
- Solve addition problems involving mixed time units (e.g., 2 hours 30 minutes + 1 hour 15 minutes) with 80% accuracy.
- Solve subtraction problems involving mixed time units (e.g., 3 hours 45 minutes - 1 hour 20 minutes) with 80% accuracy.
- Explain the process of regrouping when subtracting mixed time units, using examples, in their own words.
- Apply addition and subtraction of mixed time units to solve real-world problems involving time durations, demonstrating the correct operation in at least 3 out of 4 scenarios.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Define and identify compound, independent, and dependent events.
Construct tree diagrams and organized lists to represent the sample space of a compound event.
Apply the Fundamental Counting Principle to calculate the total number of outcomes.
Differentiate between problems with replacement and without replacement.
Calculate the total number of outcomes for multi-stage experiments.
Solve real-world problems involving the number of outcomes for compound events.
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This tutorial will teach you how to systematically count the total number of possible results, or 'outcomes,' for si...
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Key Concepts & Vocabulary
TermDefinitionExample
OutcomeA single possible result of a probability experiment.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.Drawing the ace of spades from a standard deck of 52 cards.
Compound EventAn event that consists of two or more simple events.Flipping a coin AND rolling a die. The outcome (Heads, 6) is one result of this compound event.
Independent EventsTwo events where the outcome of the first event does NOT affect the outcome of the second event.Flipping a coin and then rolling a die. The coin's result doesn't change the die's possible outcomes.
Dependent EventsTw...
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Core Formulas
The Fundamental Counting Principle (Multiplication Rule)
If event A has $m$ possible outcomes and event B has $n$ possible outcomes, then there are $m \times n$ total possible outcomes for event A followed by event B.
This is the primary method for finding the total number of outcomes without listing them all. Use it when an experiment consists of multiple stages or parts. Simply multiply the number of outcomes for each stage.
Tree Diagrams
A visual method to list all possible outcomes of a compound event. Each 'branch' represents a possible outcome for a simple event.
Use this method when you need to see and list every single possible outcome, not just the total number. It is most effective for experiments with a small number of stages and outcomes.
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Challenging
A password must be 4 characters long. The first character must be a letter (A-Z), and the remaining three characters must be digits (0-9). Repetition of digits is allowed. How many different passwords can be created?
A.260
B.26,000
C.18,720
D.23,400
Challenging
A license plate has 3 letters followed by 3 digits. The first letter cannot be 'O' or 'I'. The first digit cannot be '0'. Repetition of letters is not allowed, but repetition of digits is allowed. How many different license plates are possible?
A.12,960,000
B.11,232,000
C.14,040,000
D.12,420,000
Challenging
A group of 4 friends (Amy, Ben, Chloe, Dan) are sitting in a row of four seats. How many different seating arrangements are possible if Amy and Ben must sit next to each other?
A.6
B.24
C.12
D.8
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Frequently asked questions
What grade level is "Compound events: find the number of outcomes"?
Compound events: find the number of outcomes is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Compound events: find the number of outcomes?
You'll be able to: Solve addition problems involving mixed time units (e.g., 2 hours 30 minutes + 1 hour 15 minutes) with 80% accuracy; Solve subtraction problems involving mixed time units (e.g., 3 hours 45 minutes - 1 hour 20 minutes) with 80%….
Is "Compound events: find the number of outcomes" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Compound events: find the number of outcomes?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.