Independent & Dependent Events 🔗
When we deal with more than one event happening (Compound Events), the relationship between them matters.
1. Independent Events 🔓
Two events are Independent if the occurrence of one does NOT affect the probability of the occurrence of the other.
- Example: Tossing a coin twice.
- Result of the first toss (Head) does not change the chance of getting Head in the second toss.
P(A and B) = P(A) * P(B).
2. Dependent Events 🔒
Two events are Dependent if the occurrence of one Does affect the probability of the other. This usually happens in Sampling without Replacement.
- Example: Drawing 2 cards from a deck without replacement.
- Event A: Draw a King (4/52).
- Event B: Draw another King.
- Since one King is gone, the chance for B is now (3/51).
P(B)depends onA.
Comparison 📊
Independent Events
- Outcome of A does NOT affect B
- Sampling WITH Replacement
- Example: Coin Tossing, Dice Rolling
- P(A ∩ B) = P(A) * P(B)
VS
Dependent Events
- Outcome of A AFFECTS B
- Sampling WITHOUT Replacement
- Example: Drawing cards without putting back
- P(A ∩ B) = P(A) * P(B|A)
3. Compound Events 🍹
When two or more events happen together.
- Example: Getting a Head on coin AND a 6 on die.
Test Your Knowledge
Question 1 of 3
1. If I replace the card after picking it, the events are: