Join the Most Relevant JEE Main 2025 Test Series & get 99+ percentile! Join Now
Search any question & find its solution
Question: Answered & Verified by Expert
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
MathematicsProbabilityVITEEEVITEEE 2015
Options:
  • A $P(A \cup B \cap C)$
  • B $P(A \cap B \cap C)$
  • C $P\left(\frac{C}{A} \cap B\right)$
  • D $P\left(\frac{B}{A}\right)$
Solution:
1250 Upvotes Verified Answer
The correct answer is: $P(A \cap B \cap C)$
$\mathrm{P}(\mathrm{A}) \mathrm{P}\left(\frac{\mathrm{B}}{\mathrm{A}}\right) \mathrm{P}\left(\frac{\mathrm{C}}{\mathrm{A}} \cap \mathrm{B}\right)$
$=P(A \cap B) P\left(\frac{C}{A} \cap B\right)$
$=\frac{P(A \cap B) P[C \cap(A \cap B)]}{P(A \cap B)}$
$=P(A \cap B \cap C)$

Looking for more such questions to practice?

Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.