$A$ die is thrown. Find the probability of the following event: $A$ number less than $6$ will appear.

$A$ 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

$A$ die is thrown. Find the probability of the following event: $A$ number greater than or equal to $3$ will appear.

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.

Three coins are tossed once. Find the probability of getting at most $2$ heads.

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 $1$.