Understanding the rules of probability can help us make better decisions in our daily lives. Here’s a simple breakdown of how it works:

1. Sample Spaces and Events:

   • A sample space is all the possible outcomes. For example, when you roll a die, the sample space is:
     • $S = \{1, 2, 3, 4, 5, 6\}$.
   • An event is a specific outcome. For instance, if you want to find even numbers when rolling a die, the event would be:
     • $E = \{2, 4, 6\}$.

2. Addition Rule:

   • This rule helps us find the chance of two events happening, especially when they cannot happen at the same time.
   • You can use this formula:
     • $P(A \cup B) = P(A) + P(B)$
   • Here’s an example: If you want the chance of drawing a heart or a spade from a regular deck of cards, you find it like this:
     • $P(\text{Heart} \cup \text{Spade}) = P(\text{Heart}) + P(\text{Spade}) = \frac{13}{52} + \frac{13}{52} = \frac{1}{2}$

3. Multiplication Rule:

   • This rule is useful when you want to find the probability of two independent events happening together.
   • Use this formula:
     • $P(A \cap B) = P(A) \times P(B)$
   • For example, if you flip a coin twice, the chance of getting heads both times is:
     • $P(\text{Heads}_1 \cap \text{Heads}_2) = P(\text{Heads}) \times P(\text{Heads}) = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}$

By using these rules, we can analyze risks and possible outcomes in our everyday lives better.