$A$ positive integer is selected at random and is divided by $9$. What is the probability that the remainder is not $1$?

$A$ box contains $2$ black,$4$ white,and $3$ red balls. One ball is drawn at random from the box and kept aside. From the remaining balls in the box,another ball is drawn at random and kept aside the first. This process is repeated until all the balls are drawn from the box. The probability that the balls drawn are in the sequence of $2$ black,$4$ white,and $3$ red is

There are three events $A, B, C$ one of which must and only one can happen. The odds are $8$ to $3$ against $A$ and $5$ to $2$ against $B$. Find the odds against $C$.

There are $3$ bags which are known to contain $2$ white and $3$ black balls; $4$ white and $1$ black balls and $3$ white and $7$ black balls respectively. $A$ ball is drawn at random from one of the bags and found to be a black ball. Then the probability that it was drawn from the bag containing the most black balls is

Seven chits are numbered $1$ to $7$. Three are drawn one by one with replacement. The probability that the least number on any selected chit is $5$,is

In a race,the odds in favour of horses $A, B, C,$ and $D$ are $1:3, 1:4, 1:5,$ and $1:6,$ respectively. Find the probability that one of them wins the race.