Probability
Conditional probability with matrices
MJMT_Full_Test_08
Grade 12
Question:
Let $P(A\cap B)=\frac{1}{4}$ and $P(B)=\frac{1}{3}$, where $P\!\left(\dfrac{A\cap B}{A\cup B}\right)=\dfrac{k}{22}$. Then $k$ is
Step-by-Step Solution
Key Concept: $P(A|A\cup B)=P(A\cap(A\cup B))/P(A\cup B)=P(A)/P(A\cup B)$. We need $P(A\cap B)/P(A\cup B)=(1/4)/P(A\cup B)$. Need $P(A)$: $P(A|B)=P(A\cap B)/P(B)=(1/4)/(1/3)=3/4$. $P(A\cup B)=P(A)+P(B)-P(A\cap B)=P(A)+1/3-1/4$.
$k=6$.
Correct Answer: 6