When two dice are thrown, the probability of getting an ordered pair $(x, y)$ such that $x^2+y^2 \leq 25$, where $x$ and $y$ are the numbers that show up on the two dice, is:

The probability that a person $A$ completes a work in a given time is $\frac{2}{3}$ and the probability that another person $B$ completes the same work in the same time is $\frac{3}{4}$. If both $A$ and $B$ start doing this work at the same time,then the probability that the work is completed in the given time is

The probability of choosing randomly a number $c$ from the set $\{1, 2, 3, \ldots, 9\}$ such that the quadratic equation $x^2 + 4x + c = 0$ has real roots is

If $A, B$ and $C$ are mutually exclusive and exhaustive events of a random experiment such that $P(A) = \frac{2}{3} P(B)$ and $P(B) = 2 P(C)$,then $P(A \cup C) =$

$A$ coin is tossed and a dice is rolled. The probability that the coin shows the head and the dice shows $6$ is

$A$ coin is tossed. If it shows a tail,we draw a ball from a box which contains $2$ red and $3$ black balls. If it shows a head,we throw a die. Find the sample space for this experiment.