Three randomly chosen non-negative integers $x, y$ and $z$ are found to satisfy the equation $x+y+z=10$. Then the probability that $z$ is even,is

Two fair dice are thrown simultaneously. The probability of getting the same number on both dice is $......$.

Let $A$ and $B$ be two events such that $P(\overline{A \cup B}) = \frac{1}{6}$,$P(A \cap B) = \frac{1}{4}$,and $P(\bar{A}) = \frac{1}{4}$,where $\bar{A}$ stands for the complement of event $A$. Then events $A$ and $B$ are

Two dice are rolled simultaneously. The probability that the sum of the two numbers on the dice is a prime number is:

Describe the sample space for the indicated experiment: $A$ coin is tossed and a die is thrown.

$A$ die is formed so that the probability of getting a number $i$ when it is rolled is proportional to $i$ $(i=1, 2, 3, 4, 5, 6)$. The probability of getting an odd number on the die when it is rolled is