Welcome to Bytelearn!

Let’s check out your problem:

$8$ [N$2010$/II/$7$ modified] For events $A$ and $B$, it is given that $\mathrm{P}(A)=0.7, \mathrm{P}(B)=0.6$ and $P\left(A \mid B^{\prime}\right)=0.8$. Find$\newline$(i) $\mathrm{P}\left(A \cap B^{\prime}\right)$,$\newline$(ii) $\mathrm{P}(A \cup B)$,$\newline$(iii) $\mathrm{P}\left(B^{\prime} \mid A\right)$.$\newline$For a third event $C$, it is given that $\mathrm{P}(C)=0.5$ and that $A$ and $C$ are independent.$\newline$(iv) Find $B$$1$$\newline$(v) Hence state an inequality satisfied by $B$$2$ in the form $B$$3$, where $B$$4$ and $B$$5$ are constants to be determined.