Final answer:
The probability of an event occurring within the first half-hour or the last hour of the period from 4 to 7 p.m. is 50%. This is calculated by dividing the total favorable time (90 minutes) by the total period time (180 minutes).
Step-by-step explanation:
The student is asking about the probability of an event occurring within a certain time frame. To solve this, we will consider the total time from 4 p.m. to 7 p.m. as the period of interest. This period is 3 hours long, or 180 minutes. The first half-hour refers to the time from 4 to 4:30 p.m., which is 30 minutes. The last hour is from 6 p.m. to 7 p.m., which is 60 minutes. We then add the two periods together to get the total favorable time, which is 30 minutes + 60 minutes = 90 minutes.
The probability that the time of occurrence is within the first half-hour or the last hour of the period is calculated by dividing the favorable time by the total time of the period:
Probability = Favorable Time / Total Time = 90 minutes / 180 minutes = 0.5 or 50%
Therefore, there is a 50% chance that the event will occur within the first half-hour or the last hour of the period from 4 to 7 p.m.