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If $A, B, C$ are three events associated with a random experiment, then
$P(A) P\left(\frac{B}{A}\right) P\left(\frac{C}{A} \cap B\right)$ is
Options:
$P(A) P\left(\frac{B}{A}\right) P\left(\frac{C}{A} \cap B\right)$ is
Solution:
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Verified Answer
The correct answer is:
$P(A \cap B \cap C)$
$\mathrm{P}(\mathrm{A}) \mathrm{P}\left(\frac{\mathrm{B}}{\mathrm{A}}\right) \mathrm{P}\left(\frac{\mathrm{C}}{\mathrm{A}} \cap \mathrm{B}\right)$
$=P(A \cap B) P\left(\frac{C}{A} \cap B\right)$
$=\frac{P(A \cap B) P[C \cap(A \cap B)]}{P(A \cap B)}$
$=P(A \cap B \cap C)$
$=P(A \cap B) P\left(\frac{C}{A} \cap B\right)$
$=\frac{P(A \cap B) P[C \cap(A \cap B)]}{P(A \cap B)}$
$=P(A \cap B \cap C)$
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