When two dice are thrown simultaneously,what is the probability that the sum of the numbers on the top faces is $5$?

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 $1$.

Let $A$ and $B$ be events with $P(A)=\frac{1}{3}, P(B)=\frac{1}{4}$ and $P(A \cup B)=\frac{1}{2}$. Then which of the following statements is incorrect?

$A$ box $P$ contains one white ball,three red balls and two black balls. Another box $Q$ contains two white balls,three red balls and four black balls. If one ball is drawn at random from each one of the two boxes,then the probability that the balls drawn are of different colour is

$A$ mathematics problem is given to three students $A, B$,and $C$. The probabilities of them solving the problem are $1/2, 1/3$,and $1/4$ respectively. What is the probability that the problem is solved?

Let $A$ and $B$ be events for which $P(A) = x$,$P(B) = y$,and $P(A \cap B) = z$. Then $P(\bar{A} \cap B)$ equals: