Answer:
The answer to the question is 0.43. Let's explain why.
Step-by-step explanation:
A train arrives at the station at 15-minute intervals starting from 7:00 am which makes the train arrives at;
7:00
7:15
7:30
7:45
8:00
B train arrive at 12-minute intervals starting at 7:07 means B train arrives at;
7:07
7:19
7:31
7:43
7:55
Now, let's review the chances of a passenger arrives at the station any time between 7:00 am and 8:00 am
- If the passenger arrives between 7:00 - 7:07 the passenger will get into B train which gives us the [tex]\frac{7}{60}\\[/tex] chance since an hour is 60 minutes and the passenger waited for 7 minutes.
- If the passanger arrives between 7:07 - 7:15 passenger will get into A train which gives [tex]\frac{8}{60}[/tex] chance. If we apply this to the time limits it goes by;
- Between 7:15 - 7:19 passenger will go to B destination which gives [tex]\frac{4}{60}[/tex] chance
- Between 7:19 - 7:30 passenger will go to A destination means [tex]\frac{11}{60}[/tex] chance
- Between 7:30 - 7:43 passenger will go to B destination means [tex]\frac{13}{60}[/tex] chance
- Between 7:43 - 7:45 passenger will go to A destination which gives [tex]\frac{2}{60}[/tex] chance
- Between 7:45 - 7:55 passenger will go to B destination means [tex]\frac{10}{60}[/tex] chance
- An lastly between 7:55 - 8:00 passenger will go to A destination which gives us [tex]\frac{5}{60}[/tex] chance
Now for passenger to go to A destination the total chances are:
[tex]\frac{8}{60} + \frac{11}{60} + \frac{2}{60} + \frac{5}{60} = \frac{26}{60}[/tex] = 0.43
