Question

Romeo and juliet have a date at a given time, and each will arrive at the meeting place with a delay between 0 and 1 hour, with all pairs of delays being equally likely. the first to arrive will wait for 15 minutes and will leave if the other has not yet arrived. what is the probability that they will meet

Answer 1

Answer: 9/16

Explanation:

Let
`x` be Romeo's delay and
`y` be Juliet's delay (both in hours).

Then, we need to calculate the area not bounded by the inequalities
`y\leq x+0.25` and
`y \geq x` in the unit square with vertices
`(0,0), (0,1), (1,0), (1,1)`.

This area turns out to be 9/16.