Answer
P(not the 31st day of a month) $=\frac{358}{365}\approx0.981$
Work Step by Step
The sample space: a year (365 days). So, N(S) = 365.
The event "a person does not have a birthday on the 31st day of a month" is the complement of "a person has a birthday on the 31st day of a month".
The event "birthday on the 31st day of a month" = {Jan 31, Mar 31, May 31, Jul 31, Aug 31, Oct 31, Dec 31}. So, N(31st day of a month) = 7
P(not the 31st day of a month) = 1 - P(31st day of a month) =
$1-\frac{N(\text{31st day of a month})}{N(S)}=\frac{365}{365}-\frac{7}{365}=\frac{358}{365}\approx0.981$
