I've read that you can find the Probability of A given B by using the following formula:
Pr(AB) / Pr(A)
However, the variables are independent so you find Pr(AB) by using:
Pr(AB) = Pr(A) * PR(B)
Since you use the two formulas together, don't they cancel each other out, effectively making the first formula:
Pr(A|B) = Pr(B)
I'm a bit lost
$\endgroup$2 Answers
$\begingroup$I've read that you can find the Probability of A given B by using the following formula:
$$\frac{P(AB)}{P(A)}$$
Actually, the formula is $$\frac{P(AB)}{P(B)}$$ which means you should be able to easily see that $P(A|B)=P(A)$ if $A$ and $B$ are independent.
$\endgroup$ 0 $\begingroup$$\displaystyle P(A|B) = \frac{P(A \cap B)}{P(B)}$If variables are independent then you can write $P(A\cap B) = P(A) P(B)$. If we put this in above equation we would get $$P(A|B) = \frac {P(A) P(B)}{P(B)} = P(A)$$And this equation $P(A|B) = P(A) $ clearly shows that probability of event A happening given B has already happened is exactly same as probability of happening of A only and that is what meant by independent events.
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