The probability of an impossible event,i.e.,$P(\phi)$,is

If a number $x$ is drawn randomly from the set of numbers $\{1, 2, 3, \ldots, 50\}$,then the probability that the number $x$ satisfies the inequation $x + \frac{10}{x} \leq 11$ is

The probability of hitting a target by three marksmen are $\frac{1}{2}, \frac{1}{3}$ and $\frac{1}{4}$ respectively. The probability that one and only one of them will hit the target when they fire simultaneously,is

Let $A, B$ and $C$ be three events associated with sample space $S$. $A, B$ and $C$ are pairwise independent and $P(A)=P(B)=P(C)=P$. If all of them cannot occur simultaneously,then $P(A \cup B \cup C)$ is equal to

If $\frac{1 + 3p}{3}, \frac{1 - p}{4}$ and $\frac{1 - 2p}{2}$ are the probabilities of three mutually exclusive events,then the set of all values of $p$ is

Each of $a$ and $b$ can take values $1$ or $2$ with equal probability. The probability that the equation $ax^{2} + bx + 1 = 0$ has real roots is equal to