The probability of getting a king and a spade card when two cards are drawn simultaneously from a pack of $52$ playing cards 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

Find the probability that when a hand of $7$ cards is drawn from a well-shuffled deck of $52$ cards,it contains at least $3$ Kings.

Fifteen persons,including $A$ and $B$,sit down at random at a round table. The probability that there are $4$ persons between $A$ and $B$ is

$A$ bag contains $6$ white and $4$ black balls. $A$ die is rolled once and the number of balls equal to the number obtained on the die are drawn from the bag at random. The probability that all the balls drawn are white is:

Two points are randomly chosen on the circumference of a circle of radius $r$. The probability that the distance between the two points is at least $r$ is equal to