Two dice are thrown together. The probability that the sum of the numbers is divisible by $2$ or $3$ is

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

$A$ fair die is rolled once. Let $A$ be the event of getting an integer greater than $3$ and $B$ be the event of getting an integer less than $5$. Find $P(A \cup B)$.

Let two fair six-faced dice $A$ and $B$ be thrown simultaneously. If $E_1$ is the event that die $A$ shows up $4$,$E_2$ is the event that die $B$ shows up $2$,and $E_3$ is the event that the sum of numbers on both dice is odd,then which of the following statements is $NOT$ true?

If one card is drawn at random from a pack of $52$ cards,what is the probability that it is a king or a queen (in $/13$)?

An experiment consists of rolling a die and then tossing a coin if the number on the die is even. If the number on the die is odd,the coin is tossed twice. Write the sample space for this experiment.