🎲 Probability Notes and Worksheet – GT CUET

Probability is an important topic in Modern Mathematics and frequently appears in GT CUET Quantitative Aptitude. It deals with measuring the chance or likelihood of an event happening. Probability helps in predicting outcomes in situations involving uncertainty such as tossing coins, rolling dice, or drawing cards. 📊

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📘 Basic Concepts of Probability

An experiment is an activity that produces outcomes. Each possible result of an experiment is called an outcome. The collection of all possible outcomes is called the sample space.

Example: When a coin is tossed, the sample space is:

S = {Head, Tail}

An event is a specific outcome or group of outcomes from the sample space.

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📐 Probability Formula

Probability of an Event:

P(E) = Number of Favorable Outcomes / Total Number of Outcomes

The value of probability always lies between 0 and 1.

0 ≤ P(E) ≤ 1

• 0 means the event will not occur ❌
• 1 means the event will certainly occur ✅

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🎯 Important Probability Rules

Complement Rule:

P(E') = 1 − P(E)

This means the probability that an event does not occur is equal to 1 minus the probability that it occurs.

Addition Rule (Mutually Exclusive Events):

P(A ∪ B) = P(A) + P(B)

Multiplication Rule (Independent Events):

P(A ∩ B) = P(A) × P(B)

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🎲 Common Probability Examples

1️⃣ Tossing a Coin

Sample Space: {H, T}

Probability of getting a head:

P(H) = 1/2

2️⃣ Rolling a Dice

Sample Space: {1, 2, 3, 4, 5, 6}

Probability of getting an even number:

P(Even) = 3/6 = 1/2

3️⃣ Drawing a Card from a Deck

Total cards in a deck = 52

Probability of getting a king:

P(King) = 4/52 = 1/13

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📝 Practice Worksheet Questions

1. Find the probability of getting a tail when a coin is tossed.
2. What is the probability of getting a number greater than 4 when a dice is rolled?
3. Find the probability of drawing a red card from a deck of 52 cards.
4. A bag contains 5 red balls and 3 blue balls. What is the probability of selecting a red ball?
5. Two coins are tossed. What is the probability of getting two heads?

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📈 Tips for GT CUET Preparation

• 📌 Understand sample space and events clearly.
• 📌 Memorize the basic probability formulas.
• 📌 Practice coin, dice, and card problems regularly.
• 📌 Solve worksheet questions to improve speed.
• 📌 Revise formulas before the exam.

Probability becomes easy with regular practice. Mastering this topic can help you score well in the GT CUET Mathematics section. 🚀