Hello all,
I have a maths problem that needs to be solved please!!
Can somebody tell me what the probability of seeing the time 11:11 is in 1 day on a clock based on the average person looking at their phone 74 times a day and taking into account a clock set to 12hrs and not 24hr (making the occurrence possible twice in one day)
Then if you could provide that over a week period and a month that would be great!!
I'm trying to debunk the new age hippy theory that seeing these numbers somehow holds great spiritual significance
Thanks
You can't really do this except as a kind of Fermi estimate, which is an estimate that makes no pretence of doing anything but indicate an order of magnitude. "Average" people do not look at their phones randomly. They do not look at them at all when they are asleep. They probably do not look at them while they are scrubbing their teeth.
For your purposes, you want to err on the side of underestimating so let's first assume that, except for adolescents who by definition are
NOT normal, "average people" do not so much as glance at their phones from nine in the evening until nine in the morning. We shall further assume that they glance at their phone at 24 random times during the remaining 12 hours and notice the time only once during a call. (I am rejecting the statistic of 74 because, at one minute per average call, that would mean that the average person is spending more than an hour a day on their cell phone, which means that we are discussing my daughter, not an average person. Moreover, if my daughter made 74 calls per day, that would mean that she was spending at least 12 hours a day on the phone (because she is physically unable to be on the phone for under 10 minutes).)
So in the 12 hours assumed relevant, there are 12 times 60 minutes = 720 minutes. Given the presumed randomness of phone glances, the probability of seeing 11:11 is
\(\displaystyle \dfrac{24}{720} = \dfrac{1}{30} \approx 3.3\%.\)
Which means that the probability of not seeing it on any given day is
\(\displaystyle \dfrac{29}{30} \approx 96.7\%.\)
Now making the further assumption that our exact times of glancing at the phone are independent from day to day, the probability of not seeing 11:11 over 7 days (a week according to Western reckoning although that is not a human universal) is
\(\displaystyle \left ( \dfrac{29}{30} \right )^7\)
so the probability of seeing 11:11 over a week
\(\displaystyle 1 - \left ( \dfrac{29}{30} \right )^7 \approx 21.1\%.\)
That is higher than the probability of rolling a 1 on a single roll of a fair die.
Months of course are not of equal duration, but February is the shortest month of the year so let's say a month has AT LEAST 28 days. Therefore the probability of seeing 11:11 at least once during a month is at least
\(\displaystyle 1 - \left ( \dfrac{29}{30} \right )^{28} \approx 61.3\%\)
which is very close to being 5 chances out of 8, substantially better than even money.
Your mileage may vary, but if people actually do look at their phone 74 times a day and notice the time on each of those 74 glances (neither of which is information that I am convinced is reliable), they are practically certain to see 11:11 at least once during a month.
