I have a problem which says:
Prove through statistics that:
P(A and B) = P(A) x P(B)
How do you prove this through statistics? Thank you for any help you can give me.
The symbol $\displaystyle \mathcal{P}(B|A)$ is read the probability of B given A.
The probability is calculated by $\displaystyle \mathcal{P}(B|A)=\frac{\mathcal{P}(A\cap B)}{\mathcal{P}(A)}$.
If we know that $\displaystyle A~\& B$ are independent that means $\displaystyle \mathcal{P}(B|A)=\mathcal{P}(B)$.
That would $\displaystyle \mathcal{P}(B\cap A)=\mathcal{P}(B)\mathcal{P}(A)$.