Two persons A and B agree to meet at a place between 11 to 12 noon. The first one to arrive waits for 20 minutes and then leave. if the time of their arrival be independent and at random, then the probability that A and B meet is:

A and B are persons standing in corner square as shown in the figure. They start to move on same time with equal speed, of A can move in East or South diretion and B can move in North or West diretion. If in each step they reach in next square and their choice of direction are equlity. If it is given that A and B meet in shaded region, then the probability that they have met in the top most shaded square, is

Form the pair of linear equations In the following problems and find their solutions (if they exist) by any algebraic method. :- Places A and B are 100 km apart on a highway. One car starts from A and another from B at the same time. If the cars travel in the same direction at different speeds they meet in 5 hours. If they travel towards each other, they meet in 1 hour. What are the speeds of the two cars ?

A chess game between two grandmasters X and Y is won by whoever first wins a total of two games. X's chances of winning or loosing any perticular game are a, b and c, respectively. The games are independent and a+b+c=1. The probability that Y wins the match after the 4th game, is

A manufacturer has three machine operators A, B and C. The first operator A produces 1% defective items, where as the other two operators B and C produce 5% and 7% defective items respectively. A is on the job for 50% of the time, B is on the job for 30% of the time and C is on the job for 20% of the time. A defective item is produced, what is the probability that it was produced by A?

A and B are two independent witnesses (i.e., there is no collision between them) in a case. The probability that A will speak the truth is x and the probability that B will speak the truth is y. A and B agree in a certain statement. Show that the probability that the statement is true is (xy)/(1-x-y+2xy) .

The probabilities of two students A and B coming to the school in time are 3/7 and 5/7 respectively. Assuming that the events, 'A coming in time' and 'B coming in time' are independent, find the probability of only one of them coming to the school in time. Write at least one advantage of coming to school in time.

Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method :-Places A and B are 80 km apart from each other on a highway. A car starts from A and another from B at the same time. If they move in the same direction they meet in 8 hours , and if they move in opposite direction, they meet in 1 hour and 20 minutes respectively. Find the speed of the cars.

Five persons entered the lift cabin on the ground floor of a 8 floor house. Suppose each of them can leave the cabin independently at any floor beginning with the first. The total number of ways in which each of the five person can leave the cabin at any one of the 7 floor, is (a) 5^(7) (b) 7^(5) (c) 35 (d) 2520