Two dice are thrown simultaneously. The probability of obtaining a total score of $5$ is

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 $1$.

$A$ 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 more than $6$ will appear.

If $A, B$ and $C$ are three events of a random experiment with $P(A)=0.4, P(B)=0.3$ and $P(A \cap B)=0.2$,then the probability that neither $A$ nor $B$ occurs is

Given $f(x) = x^2 - 5x + 4$. If a number $x$ is chosen at random from the first $20$ natural numbers,then the probability that the chosen $x$ satisfies the inequality $f(x) > 10$ is