The probabilities of a student getting $I, II$ and $III$ division in an examination are respectively $\frac{1}{10}, \frac{3}{5}$ and $\frac{1}{4}$. The probability that the student fails in the examination is

Person $A$ can solve $90 \%$ of the problems given in the book and Person $B$ can solve $70 \%$. Then,the probability that at least one of them will solve the problem selected at random from the book is

Let $S_n = \sum_{k=1}^n k$ denote the sum of the first $n$ positive integers. The numbers $S_1, S_2, S_3, \ldots, S_{99}$ are written on $99$ cards. The probability of drawing a card with an even number written on it is

$A$ die is loaded such that the probability of throwing the number $i$ is proportional to its reciprocal. Then the probability that $3$ appears in a single throw is

An integer is chosen from the set $\{2k \mid -9 \leq k \leq 10\}$. The probability that the chosen integer is divisible by both $4$ and $6$ is

$A$,$B$,$C$ are three horses participating in a race. The probability of horse $A$ to win the race is twice that of horse $B$ and the probability of horse $B$ to win is twice that of horse $C$. Then the probabilities of horses $A$,$B$,and $C$ to win the race are respectively: