Understanding Independent and Dependent Events

When we talk about probability, it's important to know about independent and dependent events.

Independent Events

• Independent events are when one event has no effect on another.
• For example, if you flip a coin and then roll a die, how the coin lands does not change how the die lands.

Dependent Events

• Dependent events are different because one event can change the outcome of another.
• A good example is when you draw cards from a deck. If you take one card out and don't put it back, that first card will affect what you get when you draw again.

Conditional Probability

• For independent events, we say the probability of event A happening, given that event B has happened, is just the same as the probability of A. This is written as $P(A | B) = P(A)$.
• But for dependent events, we calculate it differently. The formula becomes $P(A | B) = \frac{P(A \cap B)}{P(B)}$. This shows how the events are connected to each other.

Knowing these ideas can really help you get better at understanding probability!