Let $A$ and $B$ are events such that $P(A)=0.3$ and $P(A \cup B)=0.8$. If $A$ and $B$ are independen

Question

Let $A$ and $B$ are events such that $P(A)=0.3$ and $P(A \cup B)=0.8$. If $A$ and $B$ are independent events, then $P(B)=\frac{m}{n}$ in the lowest form. Report m+n

Professor PC Thomas Classes · Answer

$P(A \cup B)=P(A)+P(B)-P(A \cap B)$\ $P(A \cup B)=P(A)+P(B)-P(A) 	imes P(B)$\ ( $\because A, B$ are independent events)\ $0.8=0.3+P(B)-(0.3) 	imes P(B)$\ $\Rightarrow \quad(0.7) P(B)=0.5 \Rightarrow P(B)=\frac{0.5}{0.7}=\frac{5}{7}$\