Two urns contain 5 white and 7 black balls and 3 white and 9 black balls respectively. One ball is transferred to the second urn and then one ball is drawn from the second urn. Find the probability that the first ball transferred is black, given that the ball drawn is black?

A box contains 9 red toys, 7 green toys and 9 blue toys. Each ball is of a different size. The probability that the red ball being selected is the smallest red toy, is:

N persons stand on the circumference of a circle at distinct points. Each possible pair of persons, not standing next to each other, sings a two-minute song one pair after the other. If the total time taken for singing is 28 minutes, what is N?

Tickets numbered 1 to 20 are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of 3 or 5?

Let x = 3^a + 3^b, where a and b are chosen independently from the integers1 through 100 inclusive (with each integer having an equal likelihood of being chosen). Compute the probability that x is an integral multiple of 5.

From 7 men and 5 ladies a committee of 4 is to be formed. If Mrs. X is not willing to join the committee in which Mr.Y is a member whereas Mr. Y is willing to join the committee only if Mrs. Z is included, how many such committees in all are possible?

Four cards are drawn at random from a pack of 52 plating cards. Find the probability of getting all the four cards of the same suit

A set of cards bearing the number 200-299 is used in a game. if card is drawn at random, what is the probability that it is divisible by:

A card is drawn from a pack of 52 cards .The probability of getting a queen of club or king of heart is

Four unit squares are chosen at random on a chessboard. What is the probability that three of them are of one colour and fourth is of opposite colour?