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Need explanation for: - Statistics and Probability - JEE Main-3

Let A and B be two non-null events such that A\subset B. Then, which of the following statements is always correct ?
 

  • Option 1)

    P(A\mid B)\leq P(A)

  • Option 2)

    P(A\mid B)\geqslant P(A)

  • Option 3)

    P(A\mid B)=1

     

  • Option 4)

    P(A\mid B)=P(B)-P(A)

 
Answers (1)
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A and B non null events (given)

A\subset B

P(A/B)=\frac{P(A\cap B)}{P(B)}=\frac{P(A)}{P(B)}

Since P(B)\leq 1

\Rightarrow \frac{P(A)}{P(B)}\geqslant P(A)


Option 1)

P(A\mid B)\leq P(A)

Option 2)

P(A\mid B)\geqslant P(A)

Option 3)

P(A\mid B)=1

 

Option 4)

P(A\mid B)=P(B)-P(A)

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