If A and B are any two events such that P(A)=25and P(A∩B)=320 then the conditional probability P(A/(A'∪B') where denotes the complement of A is equal to

P(AA1∪B1)=P(A∩(A1∪B1))P(A1∪B1)=P(A∪B1)P(A∩B¯)=P(A)−P(A∩B)1−P(A∩B)=25−3201−320=517

If A and B are any two events such that P(A)=25and P(A∩B)=320 then the conditional probability P(A/(A'∪B') where denotes the complement of A is equal to

P(AA1∪B1)=P(A∩(A1∪B1))P(A1∪B1)=P(A∪B1)P(A∩B¯)=P(A)−P(A∩B)1−P(A∩B)=25−3201−320=517

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If A and B are any two events such that $P (A) = \frac{2}{5} a n d P (A \cap B) = \frac{3}{20}$ then the conditional probability $P (A / (A' \cup B')$ where denotes the complement of A is equal to

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$\frac{11}{20}$

$\frac{5}{17}$

$\frac{8}{17}$

$\frac{1}{4}$

answer is B.

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Detailed Solution

$P (\frac{A}{A^{1} \cup B^{1}}) = \frac{P (A \cap (A^{1} \cup B^{1}))}{P (A^{1} \cup B^{1})} = \frac{P (A \cup B^{1})}{P (\bar{A \cap B})}$
$= \frac{P (A) - P (A \cap B)}{1 - P (A \cap B)} = \frac{\frac{2}{5} - \frac{3}{20}}{1 - \frac{3}{20}} = \frac{5}{17}$