What is the concept of Conditional Probability ?

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What is the concept of Conditional Probability ?

Mathematics
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the probability of A given B, written as \[P(A|B)\] is computed via \[P(A|B)=\frac{P(A\cap B)}{P(B)}\]
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: \(P(A|B)=\frac{P(A\bigcap B)}{P(B)}\)
plz explain howis this formula derived.....

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

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