The probability mass function of a random variable X is given by
$P(X = x) = \dfrac{{}^{5}C_x}{2^5}$, for $x = 0, 1, 2, 3, 4, 5$ and $= 0$, otherwise.
Then which of the following is correct?

If events A and B are such that $P(A) = \dfrac{1}{4}$, $P(A \cap B) = \dfrac{1}{10}$ and $P(A/B) = 2P(B/A)$ then $P(B) = $...........

A quantity P is related as $X^{-2}Y^{-3/2}Z^{2/5}$ where X,Y,Z are independent parameters which have fractional errors of $0.1, 0.2$ and $0.5$ respectively in measurement. The maximum fractional error in P is

The vectors $(\vec{A} + \vec{B})$ and $(\vec{A} - \vec{B})$ are perpendicular to each other. This is possible under the condition