A, B, C in order draws a card from a pack of cards, replacing them after each draw, on condition that the first who draws a spade shall win a prize : find their respective chances.

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 till 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 find the ratio a : b

Three cards are drawn at random from a pack of 52 cards. The probability of drawing cards which has a king, a queen and a jack is .....

All the spades are taken out from a pack of cards. From these cards; cards are drawn one by one without replacement till the ace of spades comes. The probability that the ace comes in the 4th draw is

A card is selected from a pack of 52 cards. (a) How many points are there in the sample space? (b) Calculate the probability that the card is an ace of spades. (c ) Calculate the probability that the card is (i) an ace (ii) black card.

Each of the n urns contains 4 white and 6 black balls. The (n+1) th urn contains 5 white and 5 black balls. One of the n+1 urns is chosen at random and two balls are drawn from it without replacement. Both the balls turn out to be black. If the probability that the (n+1) th urn was chosen to draw the balls is 1/16, then find the value of n .

There are 40 students in Class X of a school of whom 25 are girls and 15 are boys. The class teacher has to select one student as a class representative. She writes the name of each student on separate cards, the cards being identical. Then she puts cards in a box and stirs them thoroughly. She then draws one card from the box. What is the probability that the name written on the card is the name of (i) a girl? (ii) a boy?

Two fixed, identical conducting plates (a and (3), each of surface area S are charged to - Q and q, respectively, where Q > q > 0. A third identical plate ( lambda ), free to move Is located on the other side of the plate with charge q at a distance d as per figure. The third plate is released and collides with the plate f_3 . Assume the collision is elastic and the time of collision is sufficient to redistribute charge amongst beta and gamma . (a) Find the electric field acting on the plate gamma before collision. (b) Find the charges on beta and gamma after the collision. (c) Find the velocity of the plate gamma after the collision and at a distance d from the plate beta

Six balls are drawn successively from an urn containing 7 red and 9 black balls. Tell whether or not the trials of drawing balls are Bernoulli trials when after each draw the ball drawn is (i) replaced (ii) not replaced in the urn.

Football teams T_1 and T_2 have to play two games against each other. It is assumed that the outcomes of the two games are independent. The probabilities of T_1 winning. Drawing and losing a game against T_2 are (1)/(2),(1)/(6) and (1)/(3) respectively. Each team gets 3 points for a win. 1 point for a draw and 0 point for a loss in a game. Let X and Y denote the total points scored by teams T_1 and T_2 respectively. after two games.P(X>Y) is

Football teams T_1 and T_2 have to play two games against each other. It is assumed that the outcomes of the two games are independent. The probabilities of T_1 winning, drawing and losing a game against T_2 are (1)/(2),(1)/(6) and (1)/(3) respectively. Each team gets 3 points for a win. 1 point for a draw and 0 point for a loss in a game. Let X and Y denote the total points scored by teams T_1 and T_2 respectively. after two games. P(X=Y) is