NOTES

Here’s Class 10 Maths Chapter 15 Notes – Probability in Yoast-friendly, SEO-optimized format 👇

📘 Probability Class 10 Notes (Chapter 14)

🔷 Introduction

Probability helps us predict the chance of an event. In simple words, probability tells us how likely something is to happen. Therefore, this chapter helps students understand uncertainty in a mathematical way.

Moreover, people use probability in games, weather reports, business, sports, and science. As a result, this chapter has many real-life applications.

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🔷 What is Probability?

Probability measures the chance of an event happening.

For example, when you toss a coin, you may get head or tail. Thus, probability helps us measure that chance.

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🔷 Important Terms

Understanding these terms makes this chapter easier. Therefore, learn them carefully.

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✔ Experiment

An action that produces results is called an experiment.

For example:

• Tossing a coin
• Rolling a dice
• Picking a card

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✔ Outcome

A possible result of an experiment is called an outcome.

For example:

When you toss a coin:

Head or Tail

These are outcomes.

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✔ Event

A group of one or more outcomes is called an event.

For example:

Getting an even number on a dice.

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✔ Sample Space

The set of all possible outcomes is called sample space.

Represented by:$$S$$S

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Example of Sample Space

Tossing one coin:

$$S=\{H,T\}$$S={H,T}

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Rolling one dice:

$$S=\{1,2,3,4,5,6\}$$S={1,2,3,4,5,6}

Thus, sample space contains all possible outcomes.

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🔷 Formula of Probability

The probability of an event is:$$P(E)=\frac{Number\ of\ favourable\ outcomes}{Total\ number\ of\ possible\ outcomes}$$P(E)=Total number of possible outcomesNumber of favourable outcomes​

Therefore, probability always compares favorable outcomes with total outcomes.

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🔷 Range of Probability

Probability always lies between 0 and 1.$$0\le P(E)\le1$$0≤P(E)≤1

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Special Cases

Impossible Event

If an event cannot happen:$$P(E)=0$$P(E)=0

For example:
Getting 7 on one dice.

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Certain Event

If an event always happens:$$P(E)=1$$P(E)=1

For example:
Getting a number less than 7 on a dice.

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🔷 Probability of a Coin Toss

A coin has two possible outcomes:$$\{H,T\}$${H,T}

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Probability of Head

$$P(H)=\frac12$$P(H)=21​

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Probability of Tail

$$P(T)=\frac12$$P(T)=21​

Thus, both outcomes have equal chance.

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🔷 Probability of Rolling a Dice

Sample space:$$S=\{1,2,3,4,5,6\}$$S={1,2,3,4,5,6}

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Probability of Getting 4

Favorable outcomes = 1

Total outcomes = 6$$P(4)=\frac16$$P(4)=61​

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Probability of Getting an Even Number

Even numbers:$$\{2,4,6\}$${2,4,6}

Favorable outcomes = 3$$P(Even)=\frac36=\frac12$$P(Even)=63​=21​

Therefore, even numbers have a 50% chance.

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🔷 Probability of Drawing a Card

A standard deck has 52 cards.

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Probability of Drawing an Ace

Number of aces = 4$$P(Ace)=\frac4{52}$$P(Ace)=524​ $$=\frac1{13}$$=131​

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Probability of Drawing a King

Number of kings = 4$$P(King)=\frac1{13}$$P(King)=131​

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🔷 Complementary Events

If E is an event, then:$$P(E)+P(\bar E)=1$$P(E)+P(Eˉ)=1

Therefore, if one event happens, its complement does not happen.

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🔷 Solved Example

Example

Find the probability of getting an odd number on a dice.

Solution

Sample space:$$\{1,2,3,4,5,6\}$${1,2,3,4,5,6}

Odd numbers:$$\{1,3,5\}$${1,3,5}

Favorable outcomes = 3

Total outcomes = 6

Now use:$$P(E)=\frac36$$P(E)=63​ $$=\frac12$$=21​

Answer:

Probability = 1/2

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🔷 Important Tips

Students can score full marks by following these tips.

• Write sample space first.
• Count outcomes carefully.
• Simplify fractions.
• Check total outcomes twice.
• Use formulas clearly.

Thus, neat steps improve accuracy.

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🔷 Real-Life Uses

People use probability in many areas. For example, probability helps in:

• Weather forecasting
• Sports analysis
• Business decisions
• Insurance
• Medical research
• Games

Therefore, probability has many practical uses.