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:

Let two fair dice $A$ and $B$ be thrown. What is the probability that the number appearing on dice $A$ is greater than the number appearing on dice $B$?

Let $\Omega$ be the sample space and $A \subseteq \Omega$ be an event. Given below are two statements:
$(S1) : \text{If } P(A) = 0, \text{ then } A = \phi$
$(S2) : \text{If } P(A) = 1, \text{ then } A = \Omega$
Then:

$2$ boys and $2$ girls are in Room $X$,and $1$ boy and $3$ girls are in Room $Y$. Specify the sample space for the experiment in which a room is selected and then a person.

Two dice are thrown simultaneously. The probability of getting a multiple of $2$ on one die and a multiple of $3$ on the other die is

$A$ box contains $10$ good items and $6$ defective items. If one item is selected at random,what is the probability that it is either good or defective?