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

$A$ mathematics problem is given to three students $A, B$,and $C$. The probabilities of them solving the problem are $1/2, 1/3$,and $1/4$ respectively. What is the probability that the problem is solved?

Three coins are tossed once. Find the probability of getting no head.

Two dice are thrown and the sum of the numbers appeared on the dice is noted. If $A$ is the event of getting a prime number as their sum and $B$ is the event of getting a number greater than $8$ as their sum,then $P(A \cap \overline{B})=$

Three coins are tossed once. Let $A$ denote the event 'three heads show',$B$ denote the event 'two heads and one tail show',$C$ denote the event 'three tails show',and $D$ denote the event 'a head shows on the first coin'. Which events are simple?

$A$ coin is tossed and a die is thrown. The probability that the outcome will be a head or a number greater than $4$ or both,is