Question

Let E and F be events with P(E)=$\frac{3}{5},P\left(F\right)\frac{3}{10}$ and P$(E\cap F)=\frac{1}{5}$. Are E anf F independent?

Answer 1

It given that P(E)=$\frac{3}{5},P\left(F\right)=\frac{3}{10}andP(E\cap F)=\frac{1}{5}$

Now, $P\left(E\right)P\left(F\right)=\frac{3}{5}\times \frac{3}{10}=\frac{9}{50}\ne \frac{1}{5}=P(E\cap F)$,

Therefore, E and F are not independent events.