Probabilitas 03 | Mengenal Aturan Penjumlahan | Addition Rule | Belajar Probabilitas Dasar

Introduction

In this tutorial, we will explore the Addition Rule in probability, a fundamental concept that helps us understand how to calculate the probability of events. This guide will cover mutually exclusive events, provide examples, and give practical applications to help solidify your understanding of this topic.

Step 1: Understand Mutually Exclusive Events

• Definition: Mutually exclusive events are events that cannot occur at the same time. For example, when flipping a coin, it can either land on heads or tails, but not both.
• Key Point: If two events A and B are mutually exclusive, the probability of either A or B occurring is the sum of their individual probabilities.

Step 2: Learn the Addition Rule

• Addition Rule: For mutually exclusive events A and B, the formula is: [ P(A \text{ or } B) = P(A) + P(B) ]
• Application: Use this rule when you want to find the probability of one event or another occurring, provided they cannot happen simultaneously.

Step 3: Explore Examples of Mutually Exclusive Events

• Example 1: Rolling a die

  • Events: Rolling a 2 or rolling a 5.
  • Calculation:
    • ( P(2) = \frac{1}{6} )
    • ( P(5) = \frac{1}{6} )
    • ( P(2 \text{ or } 5) = P(2) + P(5) = \frac{1}{6} + \frac{1}{6} = \frac{2}{6} = \frac{1}{3} )

• Example 2: Drawing cards from a deck

  • Events: Drawing a heart or a spade.
  • Calculation:
    • ( P(\text{Heart}) = \frac{13}{52} )
    • ( P(\text{Spade}) = \frac{13}{52} )
    • ( P(\text{Heart or Spade}) = P(\text{Heart}) + P(\text{Spade}) = \frac{13}{52} + \frac{13}{52} = \frac{26}{52} = \frac{1}{2} )

Step 4: Apply the Addition Rule in Different Scenarios

• Study Case 1: Suppose you want to find the probability of drawing either a queen or a king from a deck of cards.

  • Calculation:
    • ( P(\text{Queen}) = \frac{4}{52} )
    • ( P(\text{King}) = \frac{4}{52} )
    • ( P(\text{Queen or King}) = \frac{4}{52} + \frac{4}{52} = \frac{8}{52} = \frac{2}{13} )

• Study Case 2: Weather prediction

  • Events: Probability of raining or snowing tomorrow.
  • If ( P(\text{Rain}) = 0.3 ) and ( P(\text{Snow}) = 0.1 ):
    • ( P(\text{Rain or Snow}) = 0.3 + 0.1 = 0.4 )

Conclusion

The Addition Rule is a vital concept in probability, particularly when dealing with mutually exclusive events. By understanding how to apply this rule, you can accurately calculate the likelihood of various outcomes. To further your knowledge, consider practicing with different scenarios and examples. For more in-depth learning, check out related playlists on statistics and probability.