Q.$A$ and $B$ are independent events with $P(A)=0.3$ and $P(B)=0.6$. Find

Independence gives $P(A\cap B)=P(A)P(B)$ directly; the rest follow from the addition theorem and the conditional-probability definition. …

(i) Because $A$ and $B$ are independent,

(ii) By the addition theorem,

(iii) By definition $P(A\mid B)=\dfrac{P(A\cap B)}{P(B)}=\dfrac{0.18}{0.6}=0.3$. This equals $P(A)$, which is exactly what independence means — knowing $B$ occurred does not change the chance of $A$. …

For independent events, remember the shortcut $P(A\mid B)=P(A)$ and $P(B\mid A)=P(B)$ — no divis …

Treating the events as mutually exclusive and writing $P(A\cap B)=0$, then $P(A\cup B)=0.9$. Independent events are **no …