Grade 6
  1. Number System  1.1. Whole Numbers  1.1.1. Place Value and Face Value  1.1.2. Comparing and Ordering Numbers  1.1.3. Rounding Numbers  1.1.4. Properties of Whole Numbers (Associative, Commutative, Distributive)  1.2. Integers  1.2.1. Introduction to Integers  1.2.2. Addition and Subtraction of Integers  1.2.3. Multiplication and Division of Integers  1.2.4. Properties of Integer Operations  1.3. Fractions  1.3.1. Types of Fractions  1.3.2. Equivalent Fractions  1.3.3. Simplification of Fractions  1.3.4. Addition and Subtraction of Fractions  1.3.5. Multiplication and Division of Fractions  1.3.6. Comparing and Ordering Fractions  1.4. Decimals  1.4.1. Understanding Decimals  1.4.2. Conversion between Fractions and Decimals  1.4.3. Addition and Subtraction of Decimals  1.4.4. Multiplication and Division of Decimals  1.4.5. Comparing and Ordering Decimals
  2. Algebra  2.1. Basics of Algebra  2.1.1. Variables and Constants  2.1.2. Expressions and Equations  2.1.3. Algebraic Terms and Coefficients  2.2. Solving Simple Equations  2.2.1. Balancing Equations  2.2.2. Solving One-Step Equations  2.2.3. Solving Two-Step Equations  2.3. Patterns and Sequences  2.3.1. Identifying Patterns  2.3.2. Arithmetic Sequences
  3. Ratio and Proportion  3.1. Ratios  3.1.1. Understanding Ratios  3.1.2. Equivalent Ratios  3.1.3. Simplifying Ratios  3.2. Proportion  3.2.1. Introduction to Proportion  3.2.2. Direct and Inverse Proportions  3.3. Percentages  3.3.1. Converting Ratios to Percentages  3.3.2. Percentage Increase and Decrease  3.3.3. Discount and Profit Calculations  3.3.4. Simple Interest Calculations in Percentages in Ratio and Proportion
  4. Geometry  4.1. Basic Geometric Shapes  4.1.1. Points, Lines, and Angles  4.1.2. Types of Angles  4.1.3. Intersecting and Parallel Lines  4.2. Triangles  4.2.1. Types of Triangles  4.2.2. Properties of Triangles  4.2.3. Sum of Angles in a Triangle  4.2.4. Congruence of Triangles  4.3. Quadrilaterals  4.3.1. Types of Quadrilaterals  4.3.2. Properties of Quadrilaterals  4.4. Circles  4.4.1. Radius and Diameter  4.4.2. Circumference and Area  4.4.3. Arcs and Chords  4.4.4. Sector and Segment
  5. Mensuration  5.1. Perimeter  5.1.1. Perimeter of Simple Shapes  5.2. Area  5.2.1. Area of Rectangles and Squares  5.2.2. Area of Triangles and Parallelograms  5.2.3. Area of Composite Figures  5.2.4. Area of Trapezium  5.3. Volume  5.3.1. Volume of Cubes and Cuboids  5.3.2. Volume of Cylinders  5.3.3. Volume of Cones  5.3.4. Surface Area of Simple Solids
  6. Data Handling  6.1. Introduction to Data  6.1.1. Types of Data  6.1.2. Organizing Data  6.1.3. Frequency Distribution  6.2. Graphs and Charts  6.2.1. Bar Graphs  6.2.2. Line Graphs  6.2.3. Pictographs  6.2.4. Pie Charts  6.3. Mean, Median, and Mode  6.3.1. Calculating Mean  6.3.2. Finding Median  6.3.3. Identifying Mode  6.3.4. Range of Data in Mean, Median, and Mode
  7. Probability  7.1. Basics of Probability  7.1.1. Understanding Probability  7.1.2. Probability of Simple Events  7.1.3. Experimental and Theoretical Probability
  8. Practical Geometry  8.1. Construction of Shapes  8.1.1. Constructing Triangles  8.1.2. Constructing Quadrilaterals  8.1.3. Constructing Circles and Arcs  8.2. Symmetry  8.2.1. Line of Symmetry  8.2.2. Rotational Symmetry  8.2.3. Translational Symmetry

Grade 6 ↓


Probability


Probability is a branch of mathematics that deals with the likelihood or probability of different outcomes. It helps us understand how likely or unlikely an event is to occur. Have you ever wondered, “How likely is it to rain today?”, “Will my favorite team win the game?”, or “Am I more likely to get tails than heads when I flip a coin?” All these questions are related to probability. Let’s move on to understand it better!

Understanding probability

Probability can be thought of as a way of measuring how confident we are about something happening. The probability of an event is how likely it is to occur. In the language of mathematics, probability is a number between 0 and 1.

  • Impossible (0): If an event will never happen, its probability will be 0.
  • Certain (1): If an event is certain to occur, then its probability is 1.
  • Possible but not certain: If an event is likely to occur but not certain, then the probability is greater than 0 but less than 1.

For example, the probability of a tossed coin landing on heads is 0.5, because it has two possible outcomes - heads or tails. Both outcomes are equally likely.

Representation of probability

Partially

Probability is often expressed as fractions. For example, the probability of rolling a six on a six-sided die is 1/6 because there is only one chance of rolling a six out of a total of six numbers.

Probability = Number of successful outcomes / Total number of possible outcomes

Decimal form

The probability can also be represented as a decimal. For a dice with six faces, it is 0.1667.

Percentage form

Probability is sometimes expressed as a percentage. The same example of a die would be represented as approximately 16.67%.

Visualization of probability

Toss off

Let's look at a simple example of tossing a coin. When you toss a coin, there are two possible outcomes:

  • Head
  • Tail

Each outcome has an equal chance of occurring, so:

Probability of getting head = 1/2 = 0.5 = 50%
Probability of tails = 1/2 = 0.5 = 50%

The probability of tossing a coin is given by:

HeadTail

Rolling the dice

Another good example is rolling a six-sided die. The possible outcomes are the following numbers:

  • 1
  • 2
  • 3
  • 4
  • 5
  • 6

Each number has an equal chance of occurring, so the probability of each number is:

Probability of getting any number = 1/6 ≈ 0.1667 ≈ 16.67%
1234

The remaining results will also be similar.

Combination of events

Independent events

Independent events do not affect each other's outcomes. For example, tossing a coin and throwing a dice are independent. The probability of both getting heads and getting a six is calculated by multiplying the probabilities:

Probability of getting head = 1/2
Probability of getting 6 = 1/6
Combined probability = 1/2 * 1/6 = 1/12

Dependent events

Dependent events affect each other. For example, removing a card from a deck affects future draws. Suppose you remove an ace from a 52-card deck and do not replace it:

Probability of first ace = 4/52
There are now 51 cards left.
Probability of second ace = 3/51

More examples

A bag of marbles

Consider a bag containing 3 red, 2 blue and 5 green marbles. Let's calculate the various probabilities:

Total marbles = 3 + 2 + 5 = 10
Probability of drawing a red marble = 3/10
Probability of drawing a blue marble = 2/10 = 1/5
Probability of drawing a green marble = 5/10 = 1/2
3 red2 Blue5 green

Card games

A deck of cards contains 52 cards of 4 suits: hearts, diamonds, clubs and spades. Each suit has 13 ranks: from ace to king. Let's calculate some probabilities:

Probability of forming a heart = 13/52 = 1/4
Probability of getting a queen = 4/52 = 1/13
Probability of drawing a red card (heart or diamond) = 26/52 = 1/2

Probability in everyday life

Probability comes up in many everyday situations, such as predicting the weather or finding a book in the library:

  • The chance of rain tomorrow is 70%.
  • The chances of finding your favorite book in the library depend on how many copies of it are available.

Conclusion

Probability helps us understand uncertainty in the world. By learning how to calculate and interpret probabilities, you can make informed decisions and better understand the likelihood of different events occurring. Whether in school, playing sports, or understanding everyday events, probability is a valuable tool that applies to many aspects of life.


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Probability

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