If the variance of the first $n$ natural numbers is 10 and the variance of the first $m$ even natural numbers is 16 , then $n: m=$

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

A problem in Algebra is given to two students $A$ and $B$ whose chances of solving it are $\frac{2}{5}$ and $\frac{3}{4}$ respectively.

The probability that the problem is solved if both of them try independently is

Three dice are thrown simultaneously and the sum of the numbers appeared on them is noted. If $A$ is the event of getting a sum greater than 14 and $B$ is the event of getting a sum which is a multiple of 3 , then $P(A \cap \bar{B})+P(\bar{A} \cap B)=$