A probability question?

[insaan]

Q::Two people agree to meet at a train station between 5:00 p.m and 5:30 p.m , and they agreed that neither person will wait for the other for more than 10 minutes..If each person arrives independently at random betwen 5:00 p.m and 5:30 p.m . what is the probability that they will meet?
please give solution.

[wat]

Q::Two people agree to meet at a train station between 5:00 p.m and 5:30 p.m , and they agreed that neither person will wait for the other for more than 10 minutes..If each person arrives independently at random betwen 5:00 p.m and 5:30 p.m . what is the probability that they will meet?
please give solution.

I would draw a square with each side 30 (1 unit = 1 minute). Then, shade in the part of the square that represents X being greater than Y by 10, or Y being greater than X by 10. Both of these shapes should be triangles. Find the area of both triangles, add them together, subtract from 900 = area of square, then divide by 900. For the actual numbers:

Area of triangle where X < Y by 10: (20)*(20)*(1/2) = 200.
Area of triangle where Y < X by 10: (20)*(20)*(1/2) = 200.

Thus, total area of the triangles = 400.

--> P(within 10 minutes of each other) = 1 - (P(not within 10 minutes of each other)
= 1 - [(200/900)+(200/900)] = 500/900 = 5/9.

[insaan]

thanks for your reply
it was a nice explanaion and i got the answer very easilyand quckly