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soty2013 Group Title

What is the concept of Conditional Probability ?

  • one year ago
  • one year ago

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  1. satellite73 Group Title
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    the probability of A given B, written as \[P(A|B)\] is computed via \[P(A|B)=\frac{P(A\cap B)}{P(B)}\]

    • one year ago
  2. klimenkov Group Title
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    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: \(P(A|B)=\frac{P(A\bigcap B)}{P(B)}\)

    • one year ago
  3. soty2013 Group Title
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    plz explain howis this formula derived.....

    • one year ago
  4. klimenkov Group Title
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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.

    • one year ago
  5. soty2013 Group Title
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    Thanks

    • one year ago
  6. klimenkov Group Title
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    If you want, I will find some problems dedicated to the conditional probability.

    • one year ago
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