What is the probability that first scheme is more profitable over second (call ranging from 0:00 to 3:20)?

Question

There are two schemes in airtel mobiles.
First scheme :1 paise per second,
Second scheme :50 paise per minute,

Following conditions are given -
1) In second scheme, second minute will be started at 0:60 or 1:00,
2) 0 sec. call means to call and cut it abruptly when timer reads 0:00, this is equivalent to a call of 1 sec.
3) In first scheme 0:14 means 15 sec.

What is the probability that first scheme is more profitable over second in a call ranging from 0:00 (1 sec.) to 3:20 (201 sec.)?

Answer 1

For the calls lasting for a duration of 1sec to 49 sec 1st scheme is profitable
Then from 60 sec to 99 sec 1st scheme is profitable
Then from 120 sec to 149 sec 1st scheme is profitable
Then from 180 sec to 199 1st scheme is profitable
So total instances here are 200
And the ones where the 1st scheme is profitable is 136
Therefore required probability = 136/200 = 0.68
Or in other words for the time span mentioned the probability of the first scheme being more profitable over the 2nd is 68% assuming all the calls of different durations have equal probability of taking place.