Probability
Mutually Exclusive vs Independent Events
Grade Class 12
Question:
Given $P(A)=0.5$, $P(A\cup B)=0.8$. If $A$ and $B$ are mutually exclusive, $P(B)=p$. If $A$ and $B$ are independent, $P(B)=q$. Find $q/p$.
Step-by-Step Solution
Key Concept: Mutually exclusive: $P(A\cup B)=P(A)+P(B)$. Independent: $P(A\cup B)=P(A)+P(B)-P(A)P(B)$.
Mutually exclusive: $p=0.8-0.5=0.3$. Independent: $0.8=0.5+q-0.5q$; $0.3=0.5q$; $q=0.6$. $q/p=0.6/0.3=2$.
Correct Answer: 2