Jurong Pioneer Junior College H2 Math papers, with video solutions

[Leave your answers in fraction]

The events $A$ and $B$ are such that $\mathrm{P}\left( A|B \right)=\frac{7}{10}$, $\mathrm{P}\left( B|A \right)=\frac{4}{15}$ and $\mathrm{P}\left( A\cup B \right)=\frac{3}{5}$.

Find the exact values of

1. $\mathrm{P}\left( A\cap B \right)$,

   [3]

2. $\mathrm{P}\left( A'\cap B \right)$.

   [2]

Find a third event $C$, it is given that $\mathrm{P}\left( C \right)=\frac{3}{10}$ and that $A$ and $C$ are independent.

3. Find $\mathrm{P}\left( A'\cap C \right)$.

   [2]

4. Hence state an inequality satisfied by $\mathrm{P}\left( A'\cap B\cap C \right)$.

   [1]