Final answer:
The probability that Mathew or Jack will have to wait is 100%, since they are arriving randomly within the same hour, and there are more possibilities where one arrives before the other than exactly at the same time.
Step-by-step explanation:
The question asks about the probability of Mathew or Jack having to wait to use the computer if they both arrive at random times between 5:00 and 6:00 pm. To calculate this, we visualize a square with a side of one hour, representing all possible arrival times for both individuals. If we divide the square into two triangles by drawing the line x = y from (5:00, 5:00) to (6:00, 6:00), we see that this line represents the moments when they arrive at the same time. The area outside this line will be the instances where one arrives before the other and, hence, where one of them will have to wait. The area of the entire square is 1 hour * 1 hour = 1 hour², and the area of one of the triangles is 1/2 * 1 hour * 1 hour = 1/2 hour².
Since there are two such triangles, the total probability that one person will have to wait is the combined area of these two triangles, which is 2 * (1/2 hour²) = 1 hour², which is the entire square. Therefore, the probability is 1 hour² / 1 hour² = 100%, so the correct answer is D. 100%.