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Compare Sample Spaces With and Without Replacement

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The Mathematics of Maybe: Introduction to Probability · Chapter challenge problems · 3:47

You'll learn: List numbered pairs and explain the presence or absence of repeated-number pairs.

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Compare Sample Spaces With and Without Replacement

3:47

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Compare Sample Spaces With and Without Replacement

You'll learn: List numbered pairs and explain the presence or absence of repeated-number pairs.

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Chapter challenge problems

11

Read an Eight-Section Spinner
3:50
Read an Eight-Section Spinner
You'll learn: Count single and grouped favourable sectors.
Two Dice Need Thirty-Six Ordered Outcomes
3:49
Two Dice Need Thirty-Six Ordered Outcomes
You'll learn: Build a6×6 outcome grid and find a prime sum greater than 5.
Impossible and Certain Events with Two Dice
3:47
Impossible and Certain Events with Two Dice
You'll learn: Construct events with probability 0 and 1 from the full sample space.
List Three-Coin Outcomes and Count Exactly Two Heads
3:43
List Three-Coin Outcomes and Count Exactly Two Heads
You'll learn: Extend the tree to eight equally likely complete sequences.
Add a First-Coin Condition to a Three-Coin Event
3:48
Add a First-Coin Condition to a Three-Coin Event
You'll learn: Select only paths satisfying both conditions.
Without Replacement, the Second Draw Changes
3:50
Without Replacement, the Second Draw Changes
You'll learn: Update branch counts when the first selected ball is laid aside.
Find the Probability of Two Different Colours
3:45
Find the Probability of Two Different Colours
You'll learn: Combine all ordered different-colour paths or subtract same-colour probability from 1.
Even Four-Digit Numbers Formed Without Repeating Digits
3:52
Even Four-Digit Numbers Formed Without Repeating Digits
You'll learn: List or organise equally likely arrangements and count those with an even last digit.
Guessing Exactly Two Correct Answers on Three Questions
3:59
Guessing Exactly Two Correct Answers on Three Questions
You'll learn: Organise correct/incorrect path patterns while retaining unequal branch probabilities.
Recording Only the Number of Heads Changes the Sample Space
3:41
Recording Only the Number of Heads Changes the Sample Space
You'll learn: Choose the valid set of recorded head counts and explain why competing lists fail.
Use Area to Model Where a Random Drop Lands
3:39
Use Area to Model Where a Random Drop Lands
You'll learn: Compare the circle’s area with the containing rectangle’s area.

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Sequences and their notation

4

A Sequence Is an Ordered List of Terms
3:48
A Sequence Is an Ordered List of Terms
You'll learn: Explain position, term value, ellipsis and finite versus infinite sequences.
Build Triangular Numbers by Adding the Next Row
3:35
Build Triangular Numbers by Adding the Next Row
You'll learn: Connect dot arrays with cumulative sums of natural numbers.
Odd Borders Build the Square Numbers
3:38
Odd Borders Build the Square Numbers
You'll learn: Connect successive odd additions with enlarging square arrays.
A New Sequence Can Come from Running Totals
3:50
A New Sequence Can Come from Running Totals
You'll learn: Generate partial sums and compare them with the original terms.