🎲 Class 10 Maths Chapter 15: Probability – Notes & Blog Post

 

📘 Introduction to Probability

Probability is the measure of chance or likelihood of an event happening. It helps us predict outcomes in uncertain situations—like tossing a coin, rolling a die, or drawing a card.

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🔢 1. Key Terms

📝 Note: The value of probability lies between 0 and 1.

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🎯 2. Types of Events

• Sure Event: Probability = 1 (Event is certain to happen)

• Impossible Event: Probability = 0 (Event cannot happen)

• Equally Likely Events: All outcomes have equal chance.

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🎲 3. Examples of Classical Probability

👉 Example 1: Tossing a coin

Sample Space (S) = {Head, Tail}
P(Head) = ½, P(Tail) = ½

👉 Example 2: Rolling a die

S = {1, 2, 3, 4, 5, 6}
P(getting a 4) = 1/6
P(getting even number) = 3/6 = ½

👉 Example 3: Drawing a card from a deck of 52

P(getting a red card) = 26/52 = ½
P(getting a king) = 4/52 = 1/13

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🔐 4. Important Formulas

• $P(E) = \frac{\text{Number of favourable outcomes}}{\text{Total outcomes}}$

• $0 \leq P(E) \leq 1$

• $P(\text{not E}) = 1 - P(E)$

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💡 5. Example Problems

Q1. A card is drawn from a well-shuffled pack. What is the probability of getting a spade?

📝 Total outcomes = 52
Favourable outcomes = 13 (spades)

$$P(\text{Spade}) = \frac{13}{52} = \frac{1}{4}$$

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Q2. A die is rolled. Find the probability of getting:

a) A prime number
b) A number greater than 4

Solution:

• a) Prime numbers = 2, 3, 5 → 3 outcomes
  $P = \frac{3}{6} = \frac{1}{2}$

• b) Greater than 4 = 5, 6 → 2 outcomes
  $P = \frac{2}{6} = \frac{1}{3}$

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✅ Key Points to Remember

• Probability is always between 0 and 1.

• Sum of probabilities of all outcomes = 1

• The more favourable outcomes, the higher the chance.

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🔍 Real-Life Applications

• Weather forecasting

• Insurance risk analysis

• Business and game strategies

• Predicting chances in games like cricket, dice, cards

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📘 Summary Table

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