Hi everyone.. I solved this problem but i'm not too confident..hope somebody can check and if it's wrong, please help me solve it the right way..
Afra and Wiro takes the train to their 8:30 AM class and arrives at the station uniformly between 7:00 AM and 7:20 AM. They both agreed that they are willing to wait for one another for 5 minutes, after which they take the train and ride alone or together. Assume that they always arrive randomly during that specified period and they don't communicate whatsoever before meeting. What is the probability that they will meet and ride the train together?
*Hint given by our professor: In a cartesian plane, a square of side 20 (minutes) represents all the possibilities of the morning arrivals of Wiro and Afra at the train station. For example (01, 07) means they arrive at 7:01 and 7:07, hence they ride the train alone. Now, the probability that they will meet= Area of region of meeting divided by the area of the square.
My answer is:
There are 420 possible morning arrivals and out of those 420 possibilities, there are 105 possibilities that they arrive within 5 minutes between each other. Therefore, i concluded that the probability that they will meet each other is 0.25.
*Based on my professor's hint, i also assumed that the area of the square=420 while the area of the region of the meeting=105. Hence, 105 divided by 420 is 0.25.
Please correct me if i'm wrong..please..thanks..