Two integers $x$ and $y$ are chosen with replacement from the set $\{0, 1, 2, 3, \ldots, 10\}$. Then the probability that $|x-y| > 5$ 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

The probabilities of a problem being solved by two students are $\frac{1}{2}$ and $\frac{1}{3}$. Then the probability of the problem being solved is

The probabilities of an anti-aircraft gun shooting down an enemy plane in the first,second,and third shots are $0.6, 0.7$,and $0.1$ respectively. What is the probability that the gun shoots down the plane?

From a book containing $100$ pages,one page is selected randomly. The probability that the sum of the digits of the page number of the selected page is $11$,is

$A$ bag contains $9$ discs of which $4$ are red,$3$ are blue and $2$ are yellow. The discs are similar in shape and size. $A$ disc is drawn at random from the bag. Calculate the probability that it will be red. (in $/9$)