Let $$0 < P\left( A \right) < 1,0 < P\left( B \right) < 1$$ and
$$P\left( {A \cup B} \right) = P\left( A \right) + P\left( B \right) - P\left( A \right)P\left( B \right)$$ then

Three of six vertices of a regular hexagon are chosen at random. The probability that the triangle with three vertices is equilateral, equals

The probability of India winning a test match against West Indies is $$1/2$$. Assuming independence from match to match the probability that in a $$5$$ match series India's second win occurs at third test is

If $$\omega \,\left( { \ne 1} \right)$$ is a cube root of unity and $${\left( {1 + \omega } \right)^7} = A + B\,\omega $$ then $$A$$ and $$B$$ are respectively