Two dice are thrown simultaneously. The probability of getting two numbers whose product is even is

Let $E_{1}, E_{2}, E_{3}$ be three mutually exclusive events such that $P(E_{1}) = \frac{2+3p}{6}$,$P(E_{2}) = \frac{2-p}{8}$,and $P(E_{3}) = \frac{1-p}{2}$. If the maximum and minimum values of $p$ are $p_{1}$ and $p_{2}$,then $(p_{1} + p_{2})$ is equal to.

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

In the random experiment of tossing two unbiased dice, let $E$ be the event of getting the sum $8$ and $F$ be the event of getting even numbers on both the dice. Then:
$I. P(E) = \frac{7}{36}$
$II. P(F) = \frac{1}{3}$
Which of the following is a correct statement?

For two events $A$ and $B$,if $P(A \cup B) = \frac{5}{6}$,$P(A) = \frac{1}{6}$,and $P(B) = \frac{2}{3}$,then $A$ and $B$ are:

The probability that a number selected at random from the set of numbers $(1, 2, 3, \ldots, 100)$ is a cube,is