On Sundays my gym is open from 10.00 am until 16.00 pm(so 6 hours) and i go for exactly 120 mins. A girl that i like comes to the same gym on Sundays for exactly 75 mins.
a) if we both choose to go to the gym uniformly random in the time interval 10.00-16.00 what is the probability to meet each other.( i think that it is clear that i can choose the time to begin only in the time interval 10.00-14.00 because i have to spent exactly 2 hours in the gym and the same for the girl)
b) what is the best time for me to go to the gym so i would have the best probability to meet her?
c) what is the best time for me to go to the gym so i would have the best probability to meet her for more than 30 mins?
a) if we both choose to go to the gym uniformly random in the time interval 10.00-16.00 what is the probability to meet each other.( i think that it is clear that i can choose the time to begin only in the time interval 10.00-14.00 because i have to spent exactly 2 hours in the gym and the same for the girl)
b) what is the best time for me to go to the gym so i would have the best probability to meet her?
c) what is the best time for me to go to the gym so i would have the best probability to meet her for more than 30 mins?