Kaidah Pencacahan 1 - Aturan Penjumlahan dan Aturan Perkalian Matematika Wajib Kelas 12

Introduction

In this tutorial, we will explore the principles of counting, specifically the rules of addition and multiplication, which are essential concepts in probability theory. Understanding these rules will help you develop a solid foundation in mathematics, particularly as you prepare for more advanced topics.

Step 1: Understanding the Rule of Addition

The rule of addition is used when we have multiple ways to achieve an outcome. It states that if there are two events that cannot occur simultaneously, the total number of ways these events can occur is the sum of the individual ways.

Key Points

• Use the rule of addition when dealing with mutually exclusive events.
• Formula: If event A has m ways and event B has n ways, then the total number of ways to achieve either A or B is:

  Total ways = m + n
  

Practical Example

If you can choose between 3 types of fruits (apple, banana, orange) and 2 types of beverages (water, juice), the total combinations of choosing one fruit or one beverage is:

Total combinations = 3 (fruits) + 2 (beverages) = 5

Step 2: Understanding the Rule of Multiplication

The rule of multiplication is applied when determining the number of ways two or more independent events can occur together. It states that if one event can occur in m ways and a second event can occur independently in n ways, the total number of ways both events can occur is the product of the number of ways each event can occur.

Key Points

• Use the rule of multiplication for independent events.
• Formula: If event A has m ways and event B has n ways, then the total number of ways to achieve both A and B is:

  Total ways = m * n
  

Practical Example

If you have 3 shirts (red, blue, green) and 2 pairs of pants (black, white), the total combinations of outfits is:

Total outfits = 3 (shirts) * 2 (pants) = 6

Step 3: Combining Both Rules

In some scenarios, you may need to use both the addition and multiplication rules together. This typically occurs when determining the total possibilities across different categories where some events are independent and others are mutually exclusive.

Practical Example

Suppose you are organizing a party and have 3 types of snacks (chips, cookies, fruit) and 2 types of drinks (soda, tea). You can either choose one snack or one drink.

• Calculate snacks and drinks:
  • Snacks: 3 ways
  • Drinks: 2 ways

Using both rules:

• Total combinations of choosing one snack or one drink:

Total = 3 (snacks) + 2 (drinks) = 5

Conclusion

Understanding the rules of addition and multiplication in counting is crucial for mastering concepts related to probability. Practice applying these rules with different examples to strengthen your grasp of the material.

Next Steps

• Explore the next parts of the counting principles series for more complex scenarios.
• Engage with practice problems to apply what you've learned.