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There are exactly 114 palindromes on a digital clock in a 24 hour period. I was asked to do this problem for homework and so theres your answer.
The second hand goes around once.
66
The hour hand goes straight up 2 times a day. The minute hand goes straight up 24 times a day. They both go straight up together at the same time 2 times a day.
It will show up any number of times from 0 to 300. The expected value is 50 but the probabiluty that is shows up exactly 50 times is around 6%.