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NCERT · Ganita Manjari · Volume 1 · Chapter 7

The Mathematics of Maybe: Introduction to Probability

42 videos in this chapter

Chance, randomness and the probability scale

6 videos

Chapter 7Probability Measures How Likely Something Is3:50Probability Measures How Likely Something IsYou'll learn: Introduce uncertainty and likelihood using the chapter’s everyday questions.Chapter 7Know What Could Happen Without Knowing What Will Happen3:50Know What Could Happen Without Knowing What Will HappenYou'll learn: Explain random experiments, individual trials and possible outcomes.Chapter 7Why Can a Coin Toss Be a Fair Way to Decide?3:39Why Can a Coin Toss Be a Fair Way to Decide?You'll learn: Connect fairness to a symmetric coin and an unbiased random toss.Chapter 7Read the Probability Scale from Zero to One3:47Read the Probability Scale from Zero to OneYou'll learn: Place impossible, less likely, even-chance, more likely and certain events on a scale.Chapter 7Fractions, Decimals and Percentages Describe the Same Chance4:01Fractions, Decimals and Percentages Describe the Same ChanceYou'll learn: Translate between numerical forms and interpret probability statements.Chapter 7Explain a Likelihood Ranking Instead of Guessing a Number4:00Explain a Likelihood Ranking Instead of Guessing a NumberYou'll learn: Rank the chapter’s everyday events and explain the assumptions behind each judgement.

Experimental and theoretical probability

8 videos

Chapter 7Estimate Probability from What Actually Happened4:00Estimate Probability from What Actually HappenedYou'll learn: Define experimental probability as event frequency divided by trials.Chapter 7Run a Coin Experiment and Record the Results3:49Run a Coin Experiment and Record the ResultsYou'll learn: Organise a20-toss experiment and calculate observed relative frequencies.Chapter 7A Paper Cup Has Three Outcomes—Are They Equally Likely?3:53

Using surveys and statistical evidence

4 videos

Chapter 7Use a Survey to Estimate a Random Student’s Preference4:03Use a Survey to Estimate a Random Student’s PreferenceYou'll learn: Read a frequency table and find a probability for a randomly selected member of the observed group.Chapter 7A Sample Can Suggest What a Larger Population Prefers3:56A Sample Can Suggest What a Larger Population PrefersYou'll learn: Scale sample proportions to estimate quantities for a whole school.Chapter 7Estimate Sweet Colours and School Club Choices3:47

Sample spaces and events

6 videos

Chapter 7List Every Possible Outcome Exactly Once3:40List Every Possible Outcome Exactly OnceYou'll learn: Define a sample space S and its number of elements n(S).Chapter 7The Question Determines the Detail in a Sample Space3:52The Question Determines the Detail in a Sample SpaceYou'll learn: Refine an outcome description to match what is recorded.Chapter 7An Event Is a Selection of Outcomes3:44An Event Is a Selection of Outcomes

Tree diagrams and multi-step experiments

4 videos

Chapter 7Build a Two-Toss Tree One Branch at a Time3:46Build a Two-Toss Tree One Branch at a TimeYou'll learn: List paths from the first toss through the second toss and label complete outcomes.Chapter 7Exactly One Head and At Least One Head Are Different Events3:34Exactly One Head and At Least One Head Are Different EventsYou'll learn: Select complete paths that match the event wording.Chapter 7Fruit Colours Can Give Unequal Tree Branches3:46

Single-step probability applications

2 videos

Chapter 7Count Even Cards and Balls That Are Not Red3:39Count Even Cards and Balls That Are Not RedYou'll learn: Identify favourable outcomes in simple uniform selections and interpret not-red.Chapter 7Find Probabilities from the Repeated Letters of PEACE3:41Find Probabilities from the Repeated Letters of PEACEYou'll learn: Calculate events involving several target letters or excluding one letter.

Chapter challenge problems

12 videos

Chapter 7Read an Eight-Section Spinner3:50Read an Eight-Section SpinnerYou'll learn: Count single and grouped favourable sectors.Chapter 7Two Dice Need Thirty-Six Ordered Outcomes3:49Two Dice Need Thirty-Six Ordered OutcomesYou'll learn: Build a6×6 outcome grid and find a prime sum greater than 5.Chapter 7Impossible and Certain Events with Two Dice3:47Impossible and Certain Events with Two Dice

A Paper Cup Has Three Outcomes—Are They Equally Likely?

You'll learn: Collect landing-position data and assign empirical probabilities.

Chapter 7Reason About a Fair Die Without Running an Experiment3:47Reason About a Fair Die Without Running an ExperimentYou'll learn: Count favourable faces among six equally likely faces.

Chapter 7Count Letter Cards, Not Just Different Letters3:52Count Letter Cards, Not Just Different LettersYou'll learn: Use equally likely physical positions when a letter repeats.

Chapter 7Two Possible Results Do Not Automatically Mean Fifty-Fifty4:03Two Possible Results Do Not Automatically Mean Fifty-FiftyYou'll learn: Test whether equally likely outcomes are justified.

Chapter 7Why Experiment and Theory Can Give Different Answers3:49Why Experiment and Theory Can Give Different AnswersYou'll learn: Compare relative frequency with the fair-model probability and discuss larger experiments.

Chapter 7A Coin and Die Have No Memory3:49A Coin and Die Have No MemoryYou'll learn: Explain independence and the gambler’s fallacy.

Estimate Sweet Colours and School Club Choices

You'll learn: Calculate sample probabilities and scale proportions to population estimates.

Chapter 7Read a Tyre-Lifetime Table as Probability Evidence3:43Read a Tyre-Lifetime Table as Probability EvidenceYou'll learn: Add relevant category frequencies and divide by the observed total.

You'll learn: Represent an event as a subset of the sample space.

Chapter 7One Sample Space Can Record Numbers or Colours3:57One Sample Space Can Record Numbers or ColoursYou'll learn: List the requested integer outcomes and separate physical balls from colour categories.

Chapter 7Combine a Die Roll with a Coin Toss3:44Combine a Die Roll with a Coin TossYou'll learn: Use ordered pairs to list the outcomes of two different random actions.

Chapter 7Use a Table to Organise Choices Without Missing Any3:54Use a Table to Organise Choices Without Missing AnyYou'll learn: List combinations systematically and identify a selected subset.

Fruit Colours Can Give Unequal Tree Branches

You'll learn: Draw a weighted tree for one selection from each basket.

Chapter 7Find the Chance of Two Pens Having the Same Colour3:55Find the Chance of Two Pens Having the Same ColourYou'll learn: Use replacement to keep second-draw probabilities unchanged and combine matching-colour paths.

You'll learn: Construct events with probability 0 and 1 from the full sample space.

Chapter 7List Three-Coin Outcomes and Count Exactly Two Heads3:43List Three-Coin Outcomes and Count Exactly Two HeadsYou'll learn: Extend the tree to eight equally likely complete sequences.

Chapter 7Add a First-Coin Condition to a Three-Coin Event3:48Add a First-Coin Condition to a Three-Coin EventYou'll learn: Select only paths satisfying both conditions.

Chapter 7Without Replacement, the Second Draw Changes3:50Without Replacement, the Second Draw ChangesYou'll learn: Update branch counts when the first selected ball is laid aside.

Chapter 7Find the Probability of Two Different Colours3:45Find the Probability of Two Different ColoursYou'll learn: Combine all ordered different-colour paths or subtract same-colour probability from 1.

Chapter 7Compare Sample Spaces With and Without Replacement3:47Compare Sample Spaces With and Without ReplacementYou'll learn: List numbered pairs and explain the presence or absence of repeated-number pairs.

Chapter 7Even Four-Digit Numbers Formed Without Repeating Digits3:52Even Four-Digit Numbers Formed Without Repeating DigitsYou'll learn: List or organise equally likely arrangements and count those with an even last digit.

Chapter 7Guessing Exactly Two Correct Answers on Three Questions3:59Guessing Exactly Two Correct Answers on Three QuestionsYou'll learn: Organise correct/incorrect path patterns while retaining unequal branch probabilities.

Chapter 7Recording Only the Number of Heads Changes the Sample Space3:41Recording Only the Number of Heads Changes the Sample SpaceYou'll learn: Choose the valid set of recorded head counts and explain why competing lists fail.

Chapter 7Use Area to Model Where a Random Drop Lands3:39Use Area to Model Where a Random Drop LandsYou'll learn: Compare the circle’s area with the containing rectangle’s area.