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The simplistic answer is that August will have five Mondays if the month starts on a Saturday, Sunday or Monday. Three days out of the seven so the probability is 3/7 = 0.4286. However, that assumes that any day of the week is equally likely and that is not the case. The impact of leap years and their 2800-year cycle is to increase the probability to 0.43

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Q: What is the probability of a month of august having 5 mondays?
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