The probabilities of an anti-aircraft gun shooting down an enemy plane in the first,second,and third shots are $0.6, 0.7$,and $0.1$ respectively. What is the probability that the gun shoots down the plane?

If $\frac{1+3P}{3}$ and $\frac{1-2P}{2}$ are probabilities of two mutually exclusive events,then $P$ lies in the interval.

For any event $A$,which of the following is true?

When two dice are thrown simultaneously,find the probability of the following:
$(1)$ The numbers are the same.
$(2)$ The difference between the numbers is $1$.

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?

The probabilities of solving a specific problem independently by $A$ and $B$ are $\frac{1}{2}$ and $\frac{1}{3}$ respectively. If both try to solve the problem independently,find the probability that the problem is solved.