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AP EAMCET · Maths · Probability

If A, B are any two events of a random experiment and \(\mathrm{P}(\mathrm{B}) \neq 1\), then \(\mathrm{P}\left(\mathrm{A} \backslash \mathrm{B}^{\mathrm{C}}\right)=\)

  1. A \(\frac{\mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{A} \cap \mathrm{B})}{1-\mathrm{P}(\mathrm{B})}\)
  2. B \(\frac{\mathrm{P}(\mathrm{A})-\mathrm{P}(\mathrm{A} \cap \mathrm{B})}{1-\mathrm{P}(\mathrm{B})}\)
  3. C \(\frac{\mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{A} \cap \mathrm{B})}{1+\mathrm{P}(\mathrm{B})}\)
  4. D \(\frac{\mathrm{P}(\mathrm{A})}{1+\mathrm{P}(\mathrm{B})}\)
Verified Solution

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

\(P\left(A / B^c\right)=\frac{P\left(A \cap B^c\right)}{P\left(B^c\right)}=\frac{P(A)-P(A \cap B)}{1-P(B)}\)