Question

What is the chance that a non-leap year contains \[53\] Saturdays?

Answer 1

Hint: To calculate the chance or probability to find the possibility for a year to have \[53\]Saturdays, we first need the total sample size or the total number of days other than Saturday that have the same chances to appear and then divide the possibility or probability of the day being Saturday by the sample space (All the days of a week).
Possibility of a day being Saturday \[P(A)=\dfrac{\text{Expected Event}}{\text{Sample Size}}\]
where \[\text{Expected Event}\] is the day we want i.e. Saturday and \[\text{Sample Size}\] is the total number of days in a week.

Complete step-by-step answer:
Now the sample size is the total number of days that are in a week and i.e. \[7\].
The total number of weeks in a year is \[52\] and if multiplied by \[7\] we get \[52\times 7=364\].
Now a year has \[365\text{ }days\] hence with \[364\text{ }days\] there is still one day left and that day can be any day so the chances of that day being Saturday is:
Possibility of a day being Saturday \[P(A)=\dfrac{\text{Expected Event}}{\text{Sample Size}}\]
\[\text{Expected Event = 1}\] (Saturday) and \[\text{Sample Size = 7}\] (Monday, Tuesday, Wednesday, Thursday, Fridays, Saturday, Sunday ).
\[=\dfrac{\text{1}}{\text{7}}\]
\[\therefore \] The possibility of the day being Saturday is \[\dfrac{\text{1}}{\text{7}}\].

Note: Students may wrong when they think that all the days in the week are full accommodated to form a single year but although a year has \[52\] weeks that doesn’t mean that it can’t have extra years and that day is the expected event we want as \[52\] weeks already have \[52\] Saturday and sample size is to be \[7\] days and not \[365\] days as other Saturdays are already been accounted for.