AP EAMCET · Maths · Probability
\(A\) and \(B\) are independent events of a random experiment if and only if
- A \(\mathrm{P}(\mathrm{A} \mid \mathrm{B}) \neq \mathrm{P}(\mathrm{A} \cap \mathrm{B})\)
- B \(\mathrm{P}(\mathrm{A} \mid \mathrm{B})=\mathrm{P}(\mathrm{B} \mid \mathrm{A})\)
- C \(\mathrm{P}(\mathrm{A} \mid \mathrm{B}) \neq \mathrm{P}\left(\mathrm{A} \mid \mathrm{B}^{\mathrm{C}}\right)\)
- D \(P(A \mid B)=P\left(A \mid B^C\right)\)
Answer & Solution
Correct Answer
(D) \(P(A \mid B)=P\left(A \mid B^C\right)\)
Step-by-step Solution
Detailed explanation
Given that \(A\) and \(B\) are independent events. \(\therefore \quad P(A \cap B)=P(A) \cdot P(B)\) \(P(A \mid B)=\frac{P(A \cap B)}{P(B)}=\frac{P(A) \cdot P(B)}{P(B)}=P(A)\) ...(i) And \(P(B \mid A)=\frac{P(B \cap A)}{P(A)}=\frac{P(B) \cdot P(A)}{P(A)}=P(B)\)…
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