67
MCQ (Single Correct Answer)
If $P(A)=\frac{7}{13}, P(B)=\frac{9}{13}$ and $P(A \cap B)=\frac{4}{13}$, then $P\left(A^{\prime} / B\right)$ is equal to
A
$\frac{6}{13}$
B
$\frac{4}{13}$
C
$\frac{4}{9}$
D
$\frac{5}{9}$
68
MCQ (Single Correct Answer)
If $A$ and $B$ are such events that $P(A)>0$ and $P(B) \neq 1$, then $P\left(A^{\prime} / B^{\prime}\right)$ equals to
A
$1-P(A / B)$
B
$1-P\left(A^{\prime} / B\right)$
C
$\frac{1-P(A \cup B)}{P\left(B^{\prime}\right)}$
D
$P\left(A^{\prime}\right) / P\left(B^{\prime}\right)$
69
MCQ (Single Correct Answer)
If $A$ and $B$ are two independent events with $P(A)=\frac{3}{5}$ and $P(B)=\frac{4}{9}$, then $P\left(A^{\prime} \cap B^{\prime}\right)$ equals to
A
$\frac{4}{15}$
B
$\frac{8}{45}$
C
$\frac{1}{3}$
D
$\frac{2}{9}$
70
MCQ (Single Correct Answer)
If two events are independent, then
A
they must be mutually exclusive
B
the sum of their probabilities must be equal to 1
C
Both (a) and (b) are correct
D
None of the above is correct
71
MCQ (Single Correct Answer)
If $A$ and $B$ be two events such that $P(A)=\frac{3}{8}, P(B)=\frac{5}{8}$ and $P(A \cup B)=\frac{3}{4}$, then $P(A / B) \cdot P\left(A^{\prime} / B\right)$ is equal to
A
$\frac{2}{5}$
B
$\frac{3}{8}$
C
$\frac{3}{20}$
D
$\frac{6}{25}$