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Conditional Probability

If A, B, C ...

Question

If $A, B, C$ are three events associated with a random experiment, then $P (A) P (\frac{B}{A}) P (\frac{C}{A} \cap B)$ is

P (A \cup B \cap C)

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P (A \cap B \cap C)

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P (\frac{C}{A} \cap B)

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P (\frac{B}{A})

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Solution

The correct option is A $P (A \cap B \cap C)$
$P (A) P (\frac{B}{A}) P (\frac{C}{A} \cap B)$

$= P (A \cap B) P (\frac{C}{A} \cap B)$ .......... (using conditional probability)

$= \frac{P (A \cap B) P [C \cap (A \cap B)]}{P (A \cap B)}$

$= P (A \cap B \cap C)$ ............. (using conditional probability)

Hence, option B is correct.

Suggest Corrections

Similar questions

P (A \cup B) = P (A) + P (B) - P (A \cap B)

P (A \cup B \cup C) = P (A) + P (B) + P (C) - P (A \cap B) - P (B \cap C) - P (A \cap C) + P (A \cap B \cap C)

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P (A \cup B) = P (A) + P (B) - P (A \cap B)

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P (A \cup B \cup C) = P (A) + P (B) - P (A \cap B) - P (B \cap C) - P (A \cap C) + P (A \cap B \cap C)

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P (A \cup B) = P (A) + P (B) - P (A \cap B)

P (A \cup B \cup C) = P (A) + P (B) + P (C) - P (A \cap B) - P (B \cap C) - P (A \cap C) + P (A \cap B \cap C)

P (A \cup B) = P (A) + P (B) - P (A \cap B)

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\frac{2}{5}

\frac{4}{7}

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P (A \cup B \cup C) = P (A) + P (B) + P (C) - P (A \cap B) - P (B \cap C) - P (A \cap C) + P (A \cap B \cap C)

\frac{2}{3}

\frac{4}{9}

\frac{1}{4}

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