If A and B are two events such that P(A)=0.6, P(B)=0.5 and P(A...

$$\begin{aligned} & P(\bar{A})=1-P(A)=1-0.6=0.4 \\ & P(\bar{B})=1-P(B)=1-0.5=0.5 \end{aligned}$$ Now, $P(A \cup B)=P(A)+P(B)-P(A \cap B)=0.6+0.5-0.4=0.7$ (1) Now $P(\bar{A} \cup B)=P(\bar{A})+P(B)-P(\bar{A} \cap B)$$\begin{aligned} & =P(\bar{A})+P(B)-\{P(B)-P(A \cap B)\} \\ = & 0.4+0.5-\{0.5-0.4\}=0.8 \end{aligned}$$$Hence, statement (1) is not correct.$$\begin{aligned} & \text{ (2) } P(\bar{B} \mid \bar{A})=\frac{P(\bar{B} \cap \bar{A})}{P(\bar{A})}=\frac{P(B \cup A)^{\prime}}{P(\bar{A})}=\frac{1-P(A \cup B)}{P(\bar{A})} \\ & =\frac{1-0.7}{0.4}=0.75 . \end{aligned}$$ Hence, statement (2) is not correct.