Serangoon Junior College H2 Math papers, with video solutions

For events $A$ and $B$, it is given that $\mathrm{P}\left( A \right)=\frac{11}{20}$, $\mathrm{P}\left( B \right)=\frac{2}{5}$ and $\mathrm{P}\left( A\cap B \right)=\frac{1}{4}$.

1. Find the probability where event $A$ occurs or event $B$ occurs but not both.

   [1]

2. Find the probability where event $B$ has occurred but not $A$.

   [1]

Find a third event $C$, it is given that $\mathrm{P}\left( C \right)=\frac{1}{2}$ and that $A$ and $C$ are independent.

3. Find the range of values of $\mathrm{P}\left( A'\cap B'\cap C \right)$.

   [3]