Probability | Year 8 Mathematics (Cambridge) PDF Download

Basic Concepts of Probability

Probability is a measure of the likelihood of an event occurring. In simple terms, it helps us predict how likely something is to happen.

• Probability Scale: Ranges from 0 (impossible event) to 1 (certain event).
• Types of Events:
  • Certain Event: Probability = 1 (e.g., the sun rising tomorrow).
  • Impossible Event: Probability = 0 (e.g., drawing a card that's both red and black).

Calculating Probabilities of Events

To calculate probability, we use the formula:

• Example Calculation:
  • Rolling a fair six-sided die:
  • Favorable outcomes (rolling a 4) = 1
  • Total possible outcomes = 6
  • Probability of rolling a 4 = 1/6
• Probability Rules:
  • Complement Rule: P(not A) = 1 − P(A)
  • Addition Rule for Mutually Exclusive Events: P(A or B) = P(A) + P(B)
  • Multiplication Rule for Independent Events: P(A and B) = P(A) × P(B)

Examples

• Coin Toss Example:
  • Probability of getting heads = 1/2
  • Probability of getting tails = 1/2
•  Drawing Cards Example:
  • Probability of drawing a red card from a standard deck = 26/52 = 1/2

Summary

Probability helps us understand the chances of events happening. By calculating probabilities using simple formulas, we can make informed predictions about the likelihood of outcomes in various situations. Remembering the basic rules and practicing with examples can strengthen our understanding of probability concepts.