Independent/Dependent Events and Multiplication Rules

Tuesday, 9/24

➢ Two events are independent if the occurrence of one does not affect the other
➢ P(A and B) = P(A) * P(B)



➢ For any events: P(A and B) = P(A) * P(B|A)
→ The “|” means given(B given A)
➢ Conditional probability when P(B) does not equal 0: P(A|B) = P(A and B)/P(B)



Video

➢ P(A|B) is probability of A given that B has occurred
P(B) P(A)




➢
➢ The area in the middle(Probability of A given B) is what we are concerned with
➢ Percentage of adults who are male and alcoholic is 2.25%. What is the probability of
having an alcoholic, given that it is a male?
→ A=being alcoholic, B=being male, P(A and B)=0.0225; we need to find P(A|B)
→ P(A|B) = P(A and B)/P(B) = 0.0225/0.5(50% chance of being male or female) =
0.045 or 4.5%
→ Probability of being an alcoholic given being a male: 4.5%


➢ If P(A)=P(A|B), then A and B are independent; if they are independent, then P(A and B)
= P(A) * P(B)