Question

Xavier and Yolanda agree to meet at the sun dial at 2:00 PM. Neither, however, is particularly punctual, and their actual arrival times to sun dial are independent, and uniformly distributed between 2:00 PM and 3:00 PM. Assuming that each will wait 15 minutes for the other, use Monte Carlo simulation to estimate the probability that they will actually meet. Use 3700 as the initial seed and 10000 as the number of simulation runs.

Answer 1

The question involves using a Monte Carlo simulation to estimate the probability of Xavier and Yolanda meeting at the sun dial, given their random arrival times between 2:00 PM and 3:00 PM and a 15-minute wait time.

Step-by-step explanation:

The student is asking to estimate the probability that Xavier and Yolanda will meet at the sun dial given that they both arrive at random times between 2:00 PM and 3:00 PM and will wait for 15 minutes for the other person.

To solve this problem, a Monte Carlo simulation can be utilized with a specified number of simulation runs and an initial seed to generate random arrival times for both individuals. With the Monte Carlo simulation, we can simulate many scenarios and calculate the fraction of times they meet within the 15 minutes of their arrival to estimate the probability.

The question involves using a Monte Carlo simulation to estimate the probability of Xavier and Yolanda meeting at the sun dial, given their random arrival times between 2:00 PM and 3:00 PM and a 15-minute wait time.