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

  • Option 1)

    P(C/D)< P(C)\;

  • Option 2)

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

  • Option 3)

    \; P(C/D)=P(C)\;

  • Option 4)

    \; P(C/D)\geqslant P(C)

 

Answers (1)

As we learnt in

Conditional Probability -

 

P\left ( \frac{A}{B} \right )= \frac{P\left ( A\cap B \right )}{P\left ( B \right )}

and

P\left ( \frac{B}{A} \right )= \frac{P\left ( A\cap B \right )}{P\left ( A \right )}

 

- wherein

where P\left ( \frac{A}{B} \right ) probability of A when B already happened.

 

 P\left ( \frac{C}{D} \right ) =\frac{P\left ( C\cap D \right )}{P\left ( D \right )}

If C and d are independent events

P\left ( C\cap D \right ) =P\left ( C \right ).P\left ( D \right )

other wise if C\subseteq D

P\left ( C\cap D \right ) = P\left ( C \right )

\therefore \: P\left ( \frac{C}{D} \right )=\frac{P\left ( C \right )}{P\left ( D \right )}\geqslant P\left ( C \right )  


Option 1)

P(C/D)< P(C)\;

Incorrect option    

Option 2)

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

Incorrect option    

Option 3)

\; P(C/D)=P(C)\;

Incorrect option    

Option 4)

\; P(C/D)\geqslant P(C)

Correct option    

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