What is the Probability of getting 5 Sundays in a Month?

The probability of having 5 Sundays in a month is 7/30 for a 30-day month and 1/31 for a 31-day month.

To calculate the probability of having 5 Sundays in a month, we need to consider the total number of days in a month and the specific arrangement of days in that month. Here’s a breakdown:

Total Number of Days in a Month

On average, a month has either 30 or 31 days. Months having 28 or 29 days can’t have 5 Sundays.

Possible Configurations

For a month with 30 days, the days can be arranged in five sets of six days each (5 weeks).

For a month with 31 days, one of the weeks will have seven days.

Probability Calculation

If the month has 30 days, there are 7 possible ways to select a week with 5 Sundays (the remaining 2 days can fall on any other days).

If the month has 31 days, there is only 1 way to have 5 Sundays (as one week must have 7 days).

Equal Probability within a Week

Within the selected week, each day has an equal chance of being a Sunday, assuming a uniform distribution.

Probability of 5 Sundays

The probability of having 5 Sundays in a month depends on the total number of days in that month. For a 30-day month, the probability is 7/30​, and for a 31-day month, the probability is 1/31​, considering the equal probability of each day within the selected week.