Dependent events are situations where the result of one event influences the result of another event. It's really important to understand how these types of events work when we want to figure out probabilities correctly.

Key Differences in Probability Calculation

1. What Are Dependent Events?

   • Two events, A and B, are called dependent if the chance that B will happen changes because A has already happened.

2. How to Calculate Probability:

   • For dependent events, we use this formula:
     P(A and B) = P(A) × P(B given A)
   • In this formula, P(B given A) tells us the chance of event B happening after event A has taken place.

3. Example:

   • Imagine you're drawing cards from a deck without putting any back. If you first draw an Ace (where P(A) = 4 out of 52), the chance of drawing another Ace (P(B given A)) changes to 3 out of 51 because one Ace is already gone.
   • So, the overall probability is:
     P(A and B) = (4/52) × (3/51) = 12/2652, which is about 0.0045.

Conclusion

When we calculate probabilities for dependent events, we need to think about what has happened before. This shows why it's important to understand the different types of events in probability.