## soty2013 2 years ago What is the concept of Conditional Probability ?

1. satellite73

the probability of A given B, written as $P(A|B)$ is computed via $P(A|B)=\frac{P(A\cap B)}{P(B)}$

2. klimenkov

Example. There is a ball in the box. This ball may be black or white. The probability to take a white ball is $$\frac1{2}$$, because the probability of it to be a black ball is $$\frac12$$. But when there is a condition that you know it is black, the probability to take a white ball equals $$0$$. That is called the conditional probability. There is a formula for it: $$P(A|B)=\frac{P(A\bigcap B)}{P(B)}$$

3. soty2013

plz explain howis this formula derived.....

4. klimenkov

It is a definition of the conditional probability. It cant be proved. There is a formula for the probability of the two independent events $$A,B$$ happen at the same time: $$P(A\bigcap B)=P(A)P(B)$$ From this, if $$P(B)\ne0$$, you can divide this by $$P(B)$$ and get the formula. I wish you think about this interesting question by yourself. If you do so you will understand it deeper.

5. soty2013

Thanks

6. klimenkov

If you want, I will find some problems dedicated to the conditional probability.