$A$ 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

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

$A$ pair of dice is thrown twice in succession. The probability of getting prime numbers on both the dice in the first throw and composite numbers on both the dice in the second throw is

Let $S$ be a set containing $n$ elements. If we select $2$ subsets $A$ and $B$ of $S$ at random,then the probability that $A \cup B = S$ and $A \cap B = \phi$ is:

Two students,Anil and Ashima,appeared in an examination. The probability that Anil will qualify the examination is $0.05$ and that Ashima will qualify the examination is $0.10$. The probability that both will qualify the examination is $0.02$. Find the probability that at least one of them will not qualify the examination.

Out of the given $25$ consecutive positive integers, three integers are drawn. If the least integer among the given $25$ integers is an odd number, then the probability that the sum of the three integers drawn is an even number is