When you start learning about probability, you'll quickly run into two important rules: the addition rule and the multiplication rule. These rules are very important for figuring out probabilities, and knowing how they work can really help you solve problems.

Addition Rule

The addition rule helps you find the probability that at least one of two (or more) events happens. It’s especially useful for events that can’t happen at the same time. Here’s how it works:

• If events A and B are mutually exclusive, this means they can’t happen together. For example, when you roll a die, you can get either a 2 or a 4 but not both at the same time. The addition rule says:

  $P(A \text{ or } B) = P(A) + P(B)$

• If events A and B are not mutually exclusive, like if you draw a card that is either red or a face card, you need to make a little adjustment:

  $P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$

This adjustment is important because when you just add the probabilities of A and B, any overlap gets counted twice, so you have to subtract it out.

Multiplication Rule

Now, the multiplication rule helps you figure out the probability of two (or more) events happening together. This is useful when looking at independent or dependent events.

• For independent events, where one event doesn’t affect the other (like flipping a coin and rolling a die), you use:

  $P(A \text{ and } B) = P(A) \times P(B)$

• For dependent events, where one event affects the other (like drawing cards without putting them back), the rule changes a bit:

  $P(A \text{ and } B) = P(A) \times P(B | A)$

In this case, $P(B | A)$ is the probability of event B happening knowing that event A has already happened.

Quick Summary

1. Addition Rule:

   • Helps you find the probability of either event occurring.
   • For mutually exclusive events: $P(A \text{ or } B) = P(A) + P(B)$
   • For non-mutually exclusive events: $P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)$

2. Multiplication Rule:

   • Helps you find the probability of both events occurring.
   • For independent events: $P(A \text{ and } B) = P(A) \times P(B)$
   • For dependent events: $P(A \text{ and } B) = P(A) \times P(B | A)$

Knowing these rules is not only useful for school but also helps you make better decisions in everyday life!