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  • Need solution for RD Sharma Maths Class12 Chapter 30 Probability Exercise Fill in the Blanks Question, Question 13.

Need solution for RD Sharma Maths Class12 Chapter 30 Probability Exercise Fill in the Blanks Question, Question 13.

Answers (1)

Answer:  Independent

Given:

For two event A and B, If

P\left (A \right )=P\left (\frac{A}{B} \right ) =\frac{1}{4}

 and

P\left (\frac{B}{A} \right )=\frac{1}{2}
then A and B are …... events.

Hint:

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

Explanation:

Let A and B are two wents.
Also \mathrm{P}(\mathrm{A})=\mathrm{P}\left(\frac{\mathrm{A}}{\mathrm{B}}\right)=(*)

We know. P\left(\frac{A}{B}\right)=\frac{P(A \cap B)}{P(B)}
Put in (*)
\begin{aligned} &P(A)=\frac{P(A \cap B)}{P(B)} \\ &\Rightarrow P(A \cap B)=P(A) P(B) \end{aligned}
\therefore A and B, are independent events.

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