# What is wrong with my reasoning? Probability with casework.

Gerry goes to sleep at 11 pm each night. But he doesn't sleep very well, so he awakens at a random time between 1:00 am and 3:59 am, with each minute equally likely (including 1:00 and 3:59). He then reads the hour and minute shown on his clock as a three digit number, so 2:56 am would be 256. What is the probability that that number will be divisible by 7?

There are 37 multiples of 7 between 100 and 359. There are 359-100+1=260 numbers between 100 and 359 inclusive. Probability is 37/260. WHy is this wrong?

You are selecting from $$\{1,2,3\}{\times}\{0,1,2,3,4,5\}{\times}\{0,1,2,3,4,5,6,7,8,9\}$$
eg $$\{(1,0,0),(1,0,1),\ldots,(1,5,9),(2,0,0),\ldots(2,5,9),(3,0,0),\ldots(3,5,9)\}$$