The probability that the product of the outcomes when three dice are rolled simultaneously is divisible by $4$ is equal to

For any two events $A$ and $B$ in a sample space,which of the following is always true?

$A$ draws two cards with replacement from a pack of $52$ cards and $B$ throws a pair of dice. What is the chance that $A$ gets both cards of the same suit and $B$ gets a total of $6$?

$A$ and $B$ throw a die alternatively till one of them gets a '$6$' and wins the game. Find their respective probabilities of winning,if $A$ starts first.

There are $2$ shelves. One shelf has $5$ Physics and $3$ Biology books,and the other has $4$ Physics and $2$ Biology books. What is the probability of drawing a Physics book?

If the numbers appearing on the two throws of a fair six-faced die are $\alpha$ and $\beta$,then the probability that $x^{2}+\alpha x+\beta > 0$ for all $x \in R$ is: