Two persons A and B agree to meet at a place between 11 and 12. The first one to arrive waits for 20 min and then leave. If the time of their arrival be independent and at random, then what is the probability A and B meet?

There are some experiment in which the outcomes cannot be identified discretely. For example, an ellipse of eccentricity 2sqrt(2)//3 is inscribed in a circle and a point within the circle is chosen at random. Now, we want to find the probability that this point lies outside the ellipse. Then, the point must lie in the shaded region shown in Figure. Let the radius of the circle be a and length of minor axis of the ellipse be 2b. Given that 1 - (b^(2))/(a^(2)) = (8)/(9) or (b^(2))/(a^(2)) = (1)/(9) Then, the area of circle serves as sample space and area of the shaded region represents the area for favorable cases. Then, required probability is p= ("Area of shaded region")/("Area of circle") =(pia^(2) - piab)/(pia^(2)) = 1 - (b)/(a) = 1 - (1)/(3) = (2)/(3) Now, answer the following questions. Two persons A and B agree to meet at a place between 5 and 6 pm. The first one to arrive waits for 20 min and then leave. If the time of their arrival be independant and at random, then the probability that A and B meet is

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 probabity that A and B meet is:

In an automobile factory, certain parts are to be fixed into the chassis in a section before it moves into another section. On a given day, one of the three persons A, B and C carries out this task. A has 45% chance, B has 35% chance and C has 20% chance of doing the task. The probability that A, B and C will take more than the allotted time is (1)/(6), (1)/(10) and (1)/(20) respectively. If it is found that the time taken is more than the allotted time, what is the probability that A has done the task ?

Two friends visit a restaurant randomly during 5 pm to 6 pm . Among the two, whoever comes first waits for 15 min and then leaves. The probability that they meet is :

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

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

Suppose that the number of telephone calls coming into a telephone exchange between 10 A.M. and 11 A.M., say, X_(1) is a random variable with possion distribution with parameter 2. Similarly the number of calls arriving between 11 A.M. and 12 noon, say X_(2) also follows a poisson distribution with parameter 6. If X_(1) and X_(2) are independent, what is the probability that more than 5 calls come in between 10 A.M. and 12 noon.

The first twelve letters of the alphabet are written down at random . What is the probability that there are four letters between the A and the B?

places A and B are 80 km apart from each other on a highway. A car starts from A and other from B at the same time. If they move in the same direction, they meet in 8 hours and if they move in opposite directions, they meet in 1 hour and 20 minutes. Find the speed of the cars.

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.