Three numbers are chosen from $1$ to $30$. The probability that they are not three consecutive numbers is

Three boys and two girls stand in a queue. The probability that the number of boys ahead of every girl is at least one more than the number of girls ahead of her is:

$A$ bag contains $a$ white and $b$ black balls. Two players $A$ and $B$ alternately draw a ball from the bag,replacing the ball each time after the draw,until one of them draws a white ball and wins the game. $A$ begins the game. If the probability of $A$ winning the game is three times that of $B$,then the ratio $a : b$ is

$A$ bag contains $3$ red, $5$ black and $7$ blue balls. If three balls are drawn at random simultaneously from the bag, then the probability of getting at least two blue balls is

Three numbers are chosen at random from $1$ to $20$. The probability that the sum of the three numbers is divisible by $3$ is:

Three cards are drawn at random from a pack of $52$ cards. What is the probability of drawing three aces?