If P(A) = 1/4, P(B) = 1/3 and P(A ∩ B) = 1/5, then P(overline(B/A)) = ?

Question

If P(A) = \(\frac{1}{4},\) P(B) = \(\frac{1}{3}\) and P(A ∩ B) = \(\frac{1}{5},\) then P\((\overline{B}/\overline{A})\) = ?

A. \(\frac{11}{15}\)

B. \(\frac{11}{45}\)

C. \(\frac{23}{60}\)

D. \(\frac{37}{45}\)

Answer 1

Correct answer is C.

P(A) = \(\frac{1}{4},\) P(B) = \(\frac{1}{3}\) and P(A ∩ B) = \(\frac{1}{5},\)

\(P(\overline{B}/\overline{A})\) = \(\frac{P(\overline{A}\cap \overline{B})}{P(\overline{A})}\) = \(\frac{1-p(A \cup B)}{1-p(A)}\) = \(\frac{1-(\frac{1}{4}+\frac{1}{3}-\frac{1}{5})}{1-\frac{1}{4}}\)