$A$ number $x$ is chosen at random from the set $\{1, 2, 3, 4, ......, 100\}$. Then the probability of the event that the chosen number $x$ satisfies the inequality $\frac{(x - 10)(x - 50)}{(x - 30)} \geqslant 0$ is:

Let $S$ be the set of all quadratic equations of the form $x^2+bx+c=0$,where $b, c \in \{1, 2, 3, 4, 5, 6\}$. If an equation is selected at random from $S$,then the probability that the equation has real roots is

There are four men and six women on the city council. If one council member is selected for a committee at random,what is the probability that the selected member is a woman (in $/5$)?

Two friends $A$ and $B$ apply for a job in the same company. The probability of $A$ getting selected is $\frac{2}{5}$ and that of $B$ is $\frac{4}{7}$. Then the probability that one of them is selected is:

$A$ and $B$ are two events such that $P(A)=0.58$,$P(B)=0.32$ and $P(A \cap B)=0.28$. Then the probability that neither $A$ nor $B$ occurs is

$A$ manager decides to distribute $Rs. 20000$ between two employees $X$ and $Y$. He knows $X$ deserves more than $Y$,but does not know how much more. So,he decides to arbitrarily break $Rs. 20000$ into two parts and gives $X$ the bigger part. Then,the chance that $X$ gets twice as much as $Y$ or more is