Probablity (do I miss the bus)

[Will]

Math word problem:

You are arriving at the bus stop at 2:41 p.m. and need to arrive at your destination at 2:57 p.m.

The bus ride is a 13 minute ride.
The bus comes every 10 minutes (however, you don't know which minute of the ten minutes you are currently at)

So what are the chances that you arrive on time?

I said that have a three minute window of opportunity, but the teacher said four, because evidently I'm not late if I make it anytime in the 2:57 p.m. minute, I can live with that, but he wants to make it out of the sixteen minutes and this seems illogical to me, because my understanding of the basic equation is "what are the chances that I arrive in the window of opportunity (3 or 4 minutes) that the bus arrives (which be equation will be from 0-10 minutes -- either inclusive 11 minutes or exclusive 10 minutes).

Can someone give me some ammunition to take to class to prove to the teacher that it is not 4 out of 16?

[marley]

this is a cool problem
great job
marley

[Will]

my thought is this, if question is "Will the bus arrive on time" it WILL arrival in the NEXT ten minutes 100% guraunteed; therefore anything outside of the 100% factor is irrelevevant. So it has to be out of TEN not 16.... just my thoughts.

[allie_poo123]

i think it might be 4 out of 11 but then again i might be wrong sorry i cant be any help and im new to this so sorry

[Will]

Originally Posted by allie_poo123

i think it might be 4 out of 11 but then again i might be wrong sorry i cant be any help and im new to this so sorry

Thanks for responding!