Multiplication Theorem of Probability ✖️
The Multiplication Theorem helps calculate the probability of simultaneous occurrence of two events. It answers: "What is the probability of obtaining A AND B?"
Symbolically: P(A ∩ B) or P(AB).
Case 1: Independent Events 🔓
If outcome of A does not affect B.
P(A ∩ B) = P(A) * P(B)
Example: Independent Events 🔓
Tossing a coin AND Rolling a die.
- A (Head): 1/2.
- B (Six): 1/6.
- P(Head AND Six) = 1/2 * 1/6 = 1/12.
Case 2: Dependent Events (Conditional) 🔒
If outcome of A affects B (e.g., drawing without replacement). We use Conditional Probability.
P(A ∩ B) = P(A) * P(B | A)
(Read P(B|A) as "Probability of B given that A has happened")
Example: Dependent Events 🔒
Bag: 3 Red, 2 Blue. Draw 2 cards without replacement.
- Task: Draw Red first, then Blue.
- P(Red): 3/5. (Now 4 balls left).
- P(Blue | Red): 2/4.
- P(Both) = 3/5 * 2/4 = 6/20 = 3/10.
Comparison 📊
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