AP EAMCET · Maths · Probability
If A, B are any two events of a random experiment and \(\mathrm{P}(\mathrm{B}) \neq 1\), then \(\mathrm{P}\left(\mathrm{A} \backslash \mathrm{B}^{\mathrm{C}}\right)=\)
- A \(\frac{\mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{A} \cap \mathrm{B})}{1-\mathrm{P}(\mathrm{B})}\)
- B \(\frac{\mathrm{P}(\mathrm{A})-\mathrm{P}(\mathrm{A} \cap \mathrm{B})}{1-\mathrm{P}(\mathrm{B})}\)
- C \(\frac{\mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{A} \cap \mathrm{B})}{1+\mathrm{P}(\mathrm{B})}\)
- D \(\frac{\mathrm{P}(\mathrm{A})}{1+\mathrm{P}(\mathrm{B})}\)
Answer & Solution
Correct Answer
(B) \(\frac{\mathrm{P}(\mathrm{A})-\mathrm{P}(\mathrm{A} \cap \mathrm{B})}{1-\mathrm{P}(\mathrm{B})}\)
Step-by-step Solution
Detailed explanation
\(P\left(A / B^c\right)=\frac{P\left(A \cap B^c\right)}{P\left(B^c\right)}=\frac{P(A)-P(A \cap B)}{1-P(B)}\)
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