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satellite73
 one year ago
Best ResponseYou've already chosen the best response.0the probability of A given B, written as \[P(AB)\] is computed via \[P(AB)=\frac{P(A\cap B)}{P(B)}\]

klimenkov
 one year ago
Best ResponseYou've already chosen the best response.1Example. 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: \(P(AB)=\frac{P(A\bigcap B)}{P(B)}\)

soty2013
 one year ago
Best ResponseYou've already chosen the best response.0plz explain howis this formula derived.....

klimenkov
 one year ago
Best ResponseYou've already chosen the best response.1It 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.

klimenkov
 one year ago
Best ResponseYou've already chosen the best response.1If you want, I will find some problems dedicated to the conditional probability.
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