Given $P(A \cup B)=0.6$ and $P(A \cap B)=0.2$,the probability that exactly one of the events occurs is:

$A$ special lottery is to be held to select a student who will live in the only deluxe room available in a hostel. $100$ $III$ year,$150$ $II$ year,and $200$ $I$ year students have applied for the room. Each $III$ year student's name is placed in the lottery $3$ times,each $II$ year student's name $2$ times,and each $I$ year student's name $1$ time. The probability that a $III$ year student gets the room is:

$A$ die has two faces each with number $1$,three faces each with number $2$,and one face with number $3$. If the die is rolled once,then $P(1 \text{ or } 3)$ is

Three groups of children $A$, $B$, and $C$ contain boys and girls as given below. Group $A$ contains $3$ girls and $1$ boy, group $B$ contains $2$ girls and $2$ boys, and group $C$ contains $3$ boys and $1$ girl. If $1$ child is selected at random from each group, what is the probability that the three children selected consist of $1$ girl and $2$ boys?

Two dice are thrown. The events $A, B$ and $C$ are as follows:
$A:$ getting an even number on the first die.
$B:$ getting an odd number on the first die.
$C:$ getting the sum of the numbers on the dice $\leq 5$.
Describe the events $A$ and $B$.

Let $A$ and $B$ be two events in a random experiment. If $P(A \cap \overline{B}) = 0.1$, $P(\overline{A} \cap B) = 0.2$ and $P(B) = 0.5$, then $P(\overline{A} \cap \overline{B}) = $