Understanding independent and dependent events is important when we talk about probability.

Independent Events:

• What are they?
  Independent events are when one event happens without changing the chance of another event happening.

• Example:
  Think about flipping a coin and rolling a die. What happens when you flip the coin doesn’t change the outcome of the die roll.

• How to calculate:
  If we call the chance of Event A happening as $P(A)$ and the chance of Event B is $P(B)$, then to find the chance of both A and B happening together, we use this formula:
  $P(A \text{ and } B) = P(A) \cdot P(B)$.

Dependent Events:

• What are they?
  Dependent events are when one event affects the chance of another event happening.

• Example:
  Imagine drawing cards from a deck without putting the first card back. The card you draw first will change what’s left in the deck.

• How to calculate:
  If we still call the chance of Event A happening $P(A)$ and the chance of Event B happening after A has already happened $P(B|A)$, then we find both events happening this way:
  $P(A \text{ and } B) = P(A) \cdot P(B|A)$.

Knowing the differences between independent and dependent events is very important for getting the probability calculations right.