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?


There are 60 minutes in an hour, not 100.   So you need to exclude numbers between 160 and 199, and those between 260 and 299, from being counted.  They will not ever show up on the clock.

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 $\{(1,0,0),(1,0,1),\ldots,(1,5,9),(2,0,0),\ldots(2,5,9),(3,0,0),\ldots(3,5,9)\}$

  • $\begingroup$ so I subtract 80 right? $\endgroup$ – Max0815 Mar 15 at 0:48
  • $\begingroup$ how many of them will be multiples of seven? $\endgroup$ – Graham Kemp Mar 15 at 0:49
  • $\begingroup$ 12 needs to be subtracted from the 37 and 80 from the 260 right? $\endgroup$ – Max0815 Mar 15 at 0:49

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