Question

You’re given 3 timings, all in the format of mm:ss (29:12 for example would mean 29 minutes and 12 seconds). They are labelled as x, y and z.

When they’re all rounded to the nearest whole number, x, y and z are 29, 29 and 13 respectively, all in minutes.

Thus, when x, y and z are added together, what are the chances that the result is 72 minutes, when rounded to the nearest whole number.

Answer 1

29 + 29 + 13 = 71
The range of possible times in seconds for x is 28:30 - 29:29. Similarly for y.
The range of possible times for z is 12:30 - 13:29
The range of possible values for x + y + z = 69:30 - 72:27 which is 178 seconds long
To be recorded as 72 minutes the sum would be in the range 71:30 - 72:27 which is 58 seconds long
P(result recorded as 72 min) = 58/178

If you simply used the ranges [28.5, 29.5) [28.5, 29.5) and [12.5, 13.5)
then the sum would be in the range [69.5, 72.5)
and P(result recorded as 72 min) = 60 seconds / 180 seconds = 1/3

Using discrete times in seconds gives a slightly different answer but is also much harder to understand.