What is the probability that when one die is thrown, the number appearing on top is even

$A$ and $B$ are two events such that $P(A)=0.54$, $P(B)=0.69$ and $P(A \cap B)=0.35.$ Find $P ( A \cup B )$.

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

Let $\quad S =\left\{ M =\left[ a _{ ij }\right], a _{ ij } \in\{0,1,2\}, 1 \leq i , j \leq 2\right\}$ be a sample space and $A=\{M \in S: M$ is invertible $\}$ be an event. Then $P ( A )$ is equal to

Five horses are in a race. $Mr. \,A$ selects two of the horses at random and bets on them. The probability that $Mr.\, A$ selected the winning horse is

A pair of a dice thrown, if $5$ appears on at least one of the dice, then the probability that the sum is $10$ or greater is