The difference between the maximum value and the minimum value of the objective function $z = 3x + y$ subject to the constraints $2x + 3y \leq 6$, $x + y \geq 1$, $x \geq 0$, $y \geq 0$ is....

A random variable $X \sim B(n, p)$ follows a binomial distribution with $n = 6$. If $9P(X = 4) = P(X = 2)$, then the probability of success $p$ is..

Let X be a continuous random variable with the probability density function(p.d.f.) given by
$f(x) = \begin{cases} kx, & 0 \leq x < 1 \\ k, & 1 \leq x < 2 \\ -kx + 3k, & 2 \leq x < 3 \\ 0, & \text{otherwise} \end{cases}$
$P(2 < X \leq 3) = \cdots$

In a certain city, the ratio of men to women is $5:4$. It is found that $80\%$ of men and $90\%$ of women are literate. If a person selected at random is found to be illiterate, then the probability that the person is a man is....