If C and D are two events such that C- D and P D - 0- then the correct statement among the following is-

The correct option is B P( C/D ) ≥ P( C ) #160; P( C|D )=P( C∩ D )/P( D ) #160; as C⊂ D,P( C )⊂ P( D ) #160; ∴ P( C∩ D )=P( C ) ...

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Byju's Answer

Standard IX

Mathematics

Mathematical Statements

If C and D ...

Question

If $C a n d D$ are two events such that $C \subset D$ and $P (D) \neq 0$ , then the correct statement among the following is:

P (C / D) = P (C)

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P (C / D) \geq P (C)

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P (C / D) \leq P (C)

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P (C / D) = \frac{P (D)}{P (C)}

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Solution

The correct option is B $P (C / D) \geq P (C)$
$P (C | D) = \frac{P (C \cap D)}{P (D)}$
$a s C \subset D, P (C) \subset P (D)$
$∴ P (C \cap D) = P (C)$
$W e h a v e P (C | D) = \frac{P (C)}{P (D)}$
$A s 0 < P (D) \leq 1$
$H e n c e$
$P (C | D) \geq P (C)$

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Similar questions

In the following diagram $P_{A}, P_{B}, P_{C}, P_{D} a n d P_{E}$ be the pressure exerted by the liquid in the vessels A, B, C, D and E respectively. Find the correct order of pressure exerted by each vessel.

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If C andD are two events such that C⊂D and P(D)≠0, then the correct statement among the following is:

The correct option is B P(C/D)≥P(C) P(C|D)=P(C∩D)P(D) asC⊂D,P(C)⊂P(D) ∴P(C∩D)=P(C) WehaveP(C|D)=P(C)P(D) As0<P(D)≤1 Hence P(C|D)≥P(C)

If $C a n d D$ are two events such that $C \subset D$ and $P (D) \neq 0$ , then the correct statement among the following is:

The correct option is B $P (C / D) \geq P (C)$
$P (C | D) = \frac{P (C \cap D)}{P (D)}$
$a s C \subset D, P (C) \subset P (D)$
$∴ P (C \cap D) = P (C)$
$W e h a v e P (C | D) = \frac{P (C)}{P (D)}$
$A s 0 < P (D) \leq 1$
$H e n c e$
$P (C | D) \geq P (C)$